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Properties

Label 2520.2.ft
Level $2520$
Weight $2$
Character orbit 2520.ft
Rep. character $\chi_{2520}(421,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.ft (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 1168 576 592
Cusp forms 1136 576 560
Eisenstein series 32 0 32

Trace form

\( 576 q + 12 q^{6} - 24 q^{8} + O(q^{10}) \) \( 576 q + 12 q^{6} - 24 q^{8} - 24 q^{12} - 12 q^{18} - 48 q^{23} + 16 q^{24} + 288 q^{25} + 80 q^{26} + 32 q^{30} - 32 q^{33} - 12 q^{34} - 4 q^{36} + 48 q^{39} - 12 q^{40} + 16 q^{41} + 64 q^{44} - 24 q^{46} + 24 q^{48} - 288 q^{49} + 36 q^{52} - 16 q^{54} - 16 q^{57} - 36 q^{58} + 24 q^{62} + 96 q^{64} - 84 q^{66} - 52 q^{68} - 108 q^{72} - 28 q^{74} + 12 q^{76} - 120 q^{78} + 32 q^{80} + 16 q^{81} + 72 q^{82} - 28 q^{84} + 104 q^{86} + 96 q^{87} - 56 q^{92} + 36 q^{94} + 64 q^{95} + 108 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)