Properties

Label 2475.2.ct
Level $2475$
Weight $2$
Character orbit 2475.ct
Rep. character $\chi_{2475}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.ct (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 6 q^{3} + O(q^{10}) \) \( 848 q + 6 q^{3} - 12 q^{11} + 36 q^{12} + 392 q^{16} + 10 q^{22} + 8 q^{23} - 160 q^{26} + 24 q^{27} - 8 q^{31} - 4 q^{33} - 48 q^{36} + 28 q^{37} - 12 q^{38} + 116 q^{42} + 12 q^{47} - 84 q^{48} + 136 q^{53} - 184 q^{56} - 36 q^{58} + 132 q^{66} + 10 q^{67} - 120 q^{71} + 30 q^{77} + 64 q^{78} - 156 q^{81} + 32 q^{82} + 16 q^{86} + 30 q^{88} + 64 q^{91} - 64 q^{92} - 38 q^{93} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)