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Decomposition of \( S_{6}^{\mathrm{old}}(12) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(12) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/6/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(4)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(3)) }^{\oplus 3 } $