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Properties

Label 1040.2.er
Level $1040$
Weight $2$
Character orbit 1040.er
Rep. character $\chi_{1040}(367,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $168$
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.er (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 720 168 552
Cusp forms 624 168 456
Eisenstein series 96 0 96

Trace form

\( 168 q + O(q^{10}) \) \( 168 q + 6 q^{13} - 6 q^{17} + 12 q^{25} + 30 q^{37} - 48 q^{41} + 30 q^{45} - 12 q^{53} + 96 q^{57} + 60 q^{65} - 12 q^{73} + 84 q^{81} + 60 q^{85} - 12 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)