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Properties

Label 3120.2.if
Level $3120$
Weight $2$
Character orbit 3120.if
Rep. character $\chi_{3120}(331,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $896$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.if (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

Total New Old
Modular forms 2720 896 1824
Cusp forms 2656 896 1760
Eisenstein series 64 0 64

Trace form

\( 896 q + O(q^{10}) \) \( 896 q + 32 q^{14} - 48 q^{16} + 32 q^{20} + 24 q^{24} + 896 q^{25} - 16 q^{26} + 104 q^{28} + 80 q^{32} + 16 q^{34} - 80 q^{38} + 96 q^{44} - 72 q^{46} - 40 q^{56} + 32 q^{58} + 32 q^{59} + 96 q^{64} + 48 q^{68} + 16 q^{70} - 64 q^{71} + 96 q^{74} + 40 q^{76} + 64 q^{80} + 448 q^{81} - 128 q^{82} + 64 q^{86} + 120 q^{88} - 16 q^{91} + 96 q^{92} + 272 q^{94} - 40 q^{96} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 2}\)