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Properties

Label 3120.2.hv
Level $3120$
Weight $2$
Character orbit 3120.hv
Rep. character $\chi_{3120}(821,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1792$
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.hv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
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 1792 928
Cusp forms 2656 1792 864
Eisenstein series 64 0 64

Trace form

\( 1792 q + 12 q^{6} + O(q^{10}) \) \( 1792 q + 12 q^{6} + 24 q^{18} + 32 q^{24} - 1792 q^{25} - 24 q^{28} + 24 q^{34} - 60 q^{36} + 40 q^{42} + 32 q^{46} - 40 q^{48} + 16 q^{54} - 40 q^{58} - 80 q^{66} + 4 q^{72} + 72 q^{76} - 124 q^{78} - 120 q^{82} - 128 q^{84} - 48 q^{91} + 24 q^{94} + 84 q^{96} - 128 q^{99} + O(q^{100}) \)

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

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