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Decomposition of \( S_{12}^{\mathrm{old}}(2) \) into lower level spaces

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