Properties

Label 7600.2.he
Level $7600$
Weight $2$
Character orbit 7600.he
Rep. character $\chi_{7600}(673,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $4768$
Sturm bound $2400$

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Defining parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.he (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7600, [\chi])\).

Total New Old
Modular forms 19392 4832 14560
Cusp forms 19008 4768 14240
Eisenstein series 384 64 320

Decomposition of \(S_{2}^{\mathrm{new}}(7600, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(7600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3800, [\chi])\)\(^{\oplus 2}\)