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Decomposition of \( S_{8}^{\mathrm{old}}(4) \) into lower level spaces

\( S_{8}^{\mathrm{old}}(4) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/2/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(2)) }^{\oplus 2 } $