Results of nuclear resonance fluorescence experiments on $^{117}$Sn are reported. More than 50 $gamma$ transitions with $E_{gamma} < 4$ MeV were detected indicating a strong fragmentation of the electromagnetic excitation strength. For the first time microscopic calculations making use of a complete configuration space for low-lying states are performed in heavy odd-mass spherical nuclei. The theoretical predictions are in good agreement with the data. It is concluded that although the E1 transitions are the strongest ones also M1 and E2 decays contribute substantially to the observed spectra. In contrast to the neighboring even $^{116-124}$Sn, in $^{117}$Sn the $1^-$ component of the two-phonon $[2^+_1 otimes 3^-_1]$ quintuplet built on top of the 1/2$^+$ ground state is proved to be strongly fragmented.
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