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Properties

Label 3120.2.cb
Level $3120$
Weight $2$
Character orbit 3120.cb
Rep. character $\chi_{3120}(733,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $672$
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.cb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1040 \)
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 672 688
Cusp forms 1328 672 656
Eisenstein series 32 0 32

Trace form

\( 672 q - 672 q^{9} + O(q^{10}) \) \( 672 q - 672 q^{9} - 8 q^{10} + 8 q^{12} - 20 q^{20} + 48 q^{22} + 16 q^{26} + 16 q^{34} + 40 q^{40} - 16 q^{44} - 672 q^{49} - 56 q^{50} - 56 q^{52} + 44 q^{60} - 72 q^{62} + 16 q^{65} + 8 q^{70} + 32 q^{73} - 16 q^{75} - 32 q^{76} - 24 q^{78} + 36 q^{80} + 672 q^{81} + 8 q^{82} + 80 q^{83} + 48 q^{86} - 8 q^{88} + 8 q^{90} + 32 q^{91} - 112 q^{98} + O(q^{100}) \)

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

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