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Properties

Label 3120.2.hp
Level $3120$
Weight $2$
Character orbit 3120.hp
Rep. character $\chi_{3120}(973,\cdot)$
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.hp (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

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

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

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