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Properties

Label 2520.2.g
Level $2520$
Weight $2$
Character orbit 2520.g
Rep. character $\chi_{2520}(1261,\cdot)$
Character field $\Q$
Dimension $120$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

Total New Old
Modular forms 592 120 472
Cusp forms 560 120 440
Eisenstein series 32 0 32

Trace form

\( 120 q + 2 q^{2} - 6 q^{4} + 4 q^{7} - 10 q^{8} + O(q^{10}) \) \( 120 q + 2 q^{2} - 6 q^{4} + 4 q^{7} - 10 q^{8} + 4 q^{10} - 2 q^{14} + 2 q^{16} - 32 q^{23} - 120 q^{25} + 4 q^{26} + 2 q^{28} - 16 q^{31} - 18 q^{32} - 8 q^{34} + 20 q^{38} + 8 q^{40} - 16 q^{41} + 4 q^{44} + 24 q^{46} + 120 q^{49} - 2 q^{50} + 88 q^{52} - 2 q^{56} - 68 q^{58} + 8 q^{62} - 6 q^{64} + 28 q^{68} + 8 q^{71} + 48 q^{74} - 36 q^{76} + 24 q^{79} + 32 q^{80} + 28 q^{82} + 36 q^{86} - 12 q^{88} - 56 q^{92} + 20 q^{94} + 32 q^{95} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)