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Properties

Label 2365.2.cj
Level $2365$
Weight $2$
Character orbit 2365.cj
Rep. character $\chi_{2365}(144,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2640$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.cj (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2365, [\chi])\).

Total New Old
Modular forms 3216 2640 576
Cusp forms 3120 2640 480
Eisenstein series 96 0 96

Trace form

\( 2640 q + 440 q^{4} - 4 q^{6} - 188 q^{9} + O(q^{10}) \) \( 2640 q + 440 q^{4} - 4 q^{6} - 188 q^{9} + 24 q^{14} - 460 q^{16} + 8 q^{19} - 28 q^{20} + 48 q^{21} + 68 q^{24} + 20 q^{25} - 16 q^{26} - 48 q^{29} - 200 q^{30} - 32 q^{31} + 20 q^{34} - 56 q^{35} - 1412 q^{36} + 24 q^{39} - 20 q^{40} - 16 q^{41} - 8 q^{44} + 20 q^{45} - 56 q^{46} + 1308 q^{49} + 54 q^{50} - 8 q^{51} + 96 q^{54} + 48 q^{56} - 88 q^{59} - 140 q^{60} + 12 q^{61} + 424 q^{64} + 36 q^{65} - 112 q^{70} - 44 q^{71} + 52 q^{74} + 140 q^{75} - 48 q^{76} - 60 q^{79} + 82 q^{80} - 24 q^{81} - 504 q^{84} - 12 q^{85} - 128 q^{86} + 120 q^{89} + 38 q^{90} + 16 q^{91} - 120 q^{94} - 98 q^{95} + 256 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2365, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2365, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)