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Properties

Label 1488.2.cq
Level $1488$
Weight $2$
Character orbit 1488.cq
Rep. character $\chi_{1488}(91,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1024$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1488.cq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 496 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1488, [\chi])\).

Total New Old
Modular forms 2080 1024 1056
Cusp forms 2016 1024 992
Eisenstein series 64 0 64

Trace form

\( 1024 q + 12 q^{8} + O(q^{10}) \) \( 1024 q + 12 q^{8} - 4 q^{10} - 32 q^{14} + 8 q^{16} + 24 q^{19} + 32 q^{20} - 200 q^{32} - 24 q^{35} + 8 q^{36} + 56 q^{38} + 40 q^{40} - 80 q^{44} - 20 q^{46} - 256 q^{49} + 48 q^{50} + 16 q^{51} + 180 q^{52} + 20 q^{54} - 56 q^{56} + 140 q^{58} - 64 q^{59} - 60 q^{62} - 12 q^{64} - 96 q^{67} - 48 q^{69} - 88 q^{70} + 192 q^{71} + 320 q^{74} + 4 q^{76} + 100 q^{80} + 256 q^{81} + 40 q^{82} - 120 q^{84} + 296 q^{94} - 100 q^{96} + 88 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1488, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1488, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1488, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(496, [\chi])\)\(^{\oplus 2}\)