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Properties

Label 2520.2.gq
Level $2520$
Weight $2$
Character orbit 2520.gq
Rep. character $\chi_{2520}(1969,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.gq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
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 288 896
Cusp forms 1120 288 832
Eisenstein series 64 0 64

Trace form

\( 288 q + 2 q^{9} + O(q^{10}) \) \( 288 q + 2 q^{9} + 8 q^{15} + 14 q^{21} + 6 q^{29} + 12 q^{35} + 20 q^{39} - 30 q^{41} + 16 q^{45} - 12 q^{49} - 12 q^{55} - 72 q^{59} + 6 q^{61} + 12 q^{65} + 8 q^{69} - 24 q^{71} + 48 q^{75} - 12 q^{79} + 30 q^{81} + 54 q^{89} + 10 q^{95} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)