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Properties

Label 3120.2.kh
Level $3120$
Weight $2$
Character orbit 3120.kh
Rep. character $\chi_{3120}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1344$
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.kh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1040 \)
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 1344 1376
Cusp forms 2656 1344 1312
Eisenstein series 64 0 64

Trace form

\( 1344 q + 672 q^{9} + O(q^{10}) \) \( 1344 q + 672 q^{9} + 8 q^{10} + 16 q^{12} - 48 q^{16} + 20 q^{20} + 12 q^{22} - 16 q^{26} + 60 q^{32} + 32 q^{34} - 40 q^{40} + 60 q^{42} + 16 q^{44} + 672 q^{49} + 56 q^{50} + 56 q^{52} - 72 q^{58} + 96 q^{59} + 16 q^{60} - 36 q^{62} - 16 q^{65} + 64 q^{70} - 32 q^{73} + 16 q^{75} + 32 q^{76} + 24 q^{78} - 36 q^{80} - 672 q^{81} - 8 q^{82} - 80 q^{83} + 80 q^{88} + 16 q^{90} + 64 q^{91} + 112 q^{98} + O(q^{100}) \)

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

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