Properties

Label 2520.2.hv
Level $2520$
Weight $2$
Character orbit 2520.hv
Rep. character $\chi_{2520}(163,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $944$
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.hv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 976 1392
Cusp forms 2240 944 1296
Eisenstein series 128 32 96

Trace form

\( 944 q + 2 q^{2} - 4 q^{8} + O(q^{10}) \) \( 944 q + 2 q^{2} - 4 q^{8} - 2 q^{10} + 8 q^{11} + 4 q^{16} + 4 q^{17} - 8 q^{20} - 4 q^{25} - 12 q^{26} + 30 q^{28} - 18 q^{32} - 16 q^{35} + 4 q^{38} + 18 q^{40} + 32 q^{41} - 16 q^{43} + 20 q^{46} + 4 q^{50} + 48 q^{52} + 20 q^{56} + 2 q^{58} + 88 q^{62} + 4 q^{65} - 28 q^{67} - 4 q^{68} + 56 q^{70} - 4 q^{73} + 48 q^{76} + 4 q^{80} - 14 q^{82} + 16 q^{83} + 24 q^{86} - 16 q^{88} + 16 q^{91} + 28 q^{92} + 16 q^{97} + 10 q^{98} + O(q^{100}) \)

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

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