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Properties

Label 3120.2.ct
Level $3120$
Weight $2$
Character orbit 3120.ct
Rep. character $\chi_{3120}(941,\cdot)$
Character field $\Q(\zeta_{4})$
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.ct (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1360 896 464
Cusp forms 1328 896 432
Eisenstein series 32 0 32

Trace form

\( 896 q - 12 q^{6} + O(q^{10}) \) \( 896 q - 12 q^{6} - 12 q^{18} + 16 q^{24} + 896 q^{25} + 24 q^{28} + 24 q^{34} - 72 q^{36} - 40 q^{42} - 32 q^{46} + 40 q^{48} + 16 q^{54} + 104 q^{58} - 40 q^{66} - 108 q^{72} + 8 q^{76} + 68 q^{78} - 20 q^{84} + 48 q^{91} + 96 q^{93} + 48 q^{94} + 116 q^{96} + O(q^{100}) \)

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

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