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Properties

Label 1045.2.cn
Level $1045$
Weight $2$
Character orbit 1045.cn
Rep. character $\chi_{1045}(29,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2784$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.cn (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
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 2976 0
Cusp forms 2784 2784 0
Eisenstein series 192 192 0

Trace form

\( 2784 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} + O(q^{10}) \) \( 2784 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} - 30 q^{11} - 96 q^{14} - 42 q^{15} - 12 q^{16} - 60 q^{19} + 102 q^{20} - 90 q^{25} + 42 q^{26} - 60 q^{29} - 15 q^{30} - 54 q^{31} - 96 q^{34} - 30 q^{35} - 30 q^{36} - 120 q^{39} - 240 q^{40} - 150 q^{41} - 90 q^{44} + 42 q^{45} - 90 q^{46} + 348 q^{49} - 45 q^{50} - 60 q^{51} + 24 q^{55} + 72 q^{59} - 93 q^{60} - 60 q^{61} - 282 q^{64} - 456 q^{66} - 54 q^{69} + 33 q^{70} - 60 q^{71} - 60 q^{74} - 60 q^{79} + 30 q^{80} - 264 q^{81} - 90 q^{84} - 90 q^{85} - 96 q^{86} - 168 q^{89} + 60 q^{90} - 162 q^{91} + 120 q^{95} + 840 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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