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Properties

Label 2645.2.j
Level $2645$
Weight $2$
Character orbit 2645.j
Rep. character $\chi_{2645}(334,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2320$
Sturm bound $552$

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Defining parameters

Level: \( N \) \(=\) \( 2645 = 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2645.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2645, [\chi])\).

Total New Old
Modular forms 3000 2720 280
Cusp forms 2520 2320 200
Eisenstein series 480 400 80

Trace form

\( 2320 q + 234 q^{4} + 9 q^{5} + 18 q^{6} + 210 q^{9} + O(q^{10}) \) \( 2320 q + 234 q^{4} + 9 q^{5} + 18 q^{6} + 210 q^{9} + 13 q^{10} + 26 q^{11} + 26 q^{14} + 10 q^{15} - 158 q^{16} + 14 q^{19} - 49 q^{20} + 22 q^{21} - 372 q^{24} - 21 q^{25} + 42 q^{26} + 26 q^{29} - 19 q^{30} + 10 q^{31} - 8 q^{34} + 37 q^{35} - 122 q^{36} - 14 q^{39} + q^{40} - 10 q^{41} - 166 q^{44} + 42 q^{45} + 80 q^{49} - 25 q^{50} + 22 q^{51} - 116 q^{54} - 31 q^{55} + 116 q^{56} - 48 q^{59} - 123 q^{60} + 38 q^{61} + 78 q^{64} - 76 q^{65} + 28 q^{66} - 402 q^{70} + 116 q^{71} - 22 q^{74} - 14 q^{75} - 4 q^{76} - 42 q^{79} - 18 q^{80} - 254 q^{81} - 56 q^{84} + 129 q^{85} - 132 q^{86} + 66 q^{89} + 198 q^{90} - 76 q^{91} + 54 q^{94} + 62 q^{95} - 324 q^{96} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2645, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2645, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2645, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)