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Properties

Label 1040.2.cc
Level $1040$
Weight $2$
Character orbit 1040.cc
Rep. character $\chi_{1040}(469,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.cc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).

Total New Old
Modular forms 344 288 56
Cusp forms 328 288 40
Eisenstein series 16 0 16

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 12 q^{10} - 8 q^{16} + 16 q^{19} + 28 q^{20} - 8 q^{24} + 60 q^{30} - 48 q^{31} - 56 q^{34} + 24 q^{35} - 112 q^{36} - 32 q^{40} - 56 q^{44} - 32 q^{46} + 288 q^{49} - 12 q^{50} + 16 q^{51} + 24 q^{54} + 48 q^{56} - 68 q^{60} + 32 q^{61} + 24 q^{64} + 168 q^{66} - 32 q^{69} - 60 q^{70} + 40 q^{74} - 72 q^{75} + 152 q^{76} - 32 q^{79} + 12 q^{80} - 288 q^{81} - 56 q^{84} + 80 q^{86} + 92 q^{90} - 32 q^{94} - 48 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)