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Properties

Label 2520.2.ei
Level $2520$
Weight $2$
Character orbit 2520.ei
Rep. character $\chi_{2520}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.ei (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 320 864
Cusp forms 1120 320 800
Eisenstein series 64 0 64

Trace form

\( 320 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + O(q^{10}) \) \( 320 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 8 q^{11} + 2 q^{14} + 2 q^{16} + 16 q^{22} - 160 q^{25} - 30 q^{26} - 22 q^{28} - 2 q^{32} - 60 q^{38} - 16 q^{43} + 30 q^{44} + 10 q^{46} - 16 q^{49} + 4 q^{50} + 36 q^{52} + 32 q^{56} + 14 q^{58} - 48 q^{59} - 44 q^{64} - 8 q^{67} + 60 q^{68} - 4 q^{70} + 48 q^{73} - 14 q^{74} + 102 q^{82} + 60 q^{86} + 56 q^{88} + 24 q^{89} - 32 q^{91} - 76 q^{92} + 54 q^{94} + 30 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)