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Properties

Label 3120.2.di
Level $3120$
Weight $2$
Character orbit 3120.di
Rep. character $\chi_{3120}(547,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.di (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 576 784
Cusp forms 1328 576 752
Eisenstein series 32 0 32

Trace form

\( 576 q - 8 q^{4} - 24 q^{8} - 576 q^{9} + O(q^{10}) \) \( 576 q - 8 q^{4} - 24 q^{8} - 576 q^{9} + 8 q^{12} - 8 q^{16} + 16 q^{19} + 24 q^{20} + 8 q^{22} - 56 q^{28} - 24 q^{30} - 8 q^{34} + 48 q^{35} + 8 q^{36} + 80 q^{38} - 56 q^{40} - 32 q^{43} + 96 q^{44} + 8 q^{46} - 96 q^{47} + 32 q^{48} + 56 q^{50} + 16 q^{51} + 8 q^{52} + 96 q^{56} - 24 q^{58} + 32 q^{61} - 8 q^{64} + 48 q^{66} + 96 q^{67} + 32 q^{68} + 32 q^{69} + 32 q^{70} + 24 q^{72} + 16 q^{75} + 8 q^{76} - 136 q^{80} + 576 q^{81} - 112 q^{82} - 48 q^{84} - 96 q^{88} + 80 q^{92} + 56 q^{94} - 112 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)