Properties

Label 1045.2.cm
Level $1045$
Weight $2$
Character orbit 1045.cm
Rep. character $\chi_{1045}(41,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $1920$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.cm (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

Total New Old
Modular forms 2976 1920 1056
Cusp forms 2784 1920 864
Eisenstein series 192 0 192

Trace form

\( 1920 q + 12 q^{3} - 30 q^{6} + 36 q^{9} + O(q^{10}) \) \( 1920 q + 12 q^{3} - 30 q^{6} + 36 q^{9} - 36 q^{14} + 60 q^{17} - 24 q^{22} + 90 q^{24} - 60 q^{26} - 36 q^{27} - 30 q^{29} + 36 q^{31} - 90 q^{33} + 24 q^{34} - 246 q^{36} - 24 q^{38} + 90 q^{41} + 294 q^{42} - 168 q^{44} - 96 q^{47} - 126 q^{48} - 264 q^{49} - 60 q^{51} - 150 q^{52} - 72 q^{53} - 96 q^{58} + 138 q^{59} - 60 q^{62} + 240 q^{64} + 126 q^{66} - 36 q^{67} - 108 q^{69} - 216 q^{70} - 12 q^{71} + 144 q^{77} - 192 q^{81} + 54 q^{82} + 12 q^{86} + 144 q^{88} + 108 q^{89} - 6 q^{91} + 48 q^{93} - 480 q^{96} - 210 q^{97} - 66 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)