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Properties

Label 2365.2.bc
Level $2365$
Weight $2$
Character orbit 2365.bc
Rep. character $\chi_{2365}(1334,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1008$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.bc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1072 1008 64
Cusp forms 1040 1008 32
Eisenstein series 32 0 32

Trace form

\( 1008 q + 252 q^{4} + 2 q^{5} + 8 q^{6} + 236 q^{9} + O(q^{10}) \) \( 1008 q + 252 q^{4} + 2 q^{5} + 8 q^{6} + 236 q^{9} - 8 q^{10} - 8 q^{11} - 12 q^{14} + 6 q^{15} - 252 q^{16} + 8 q^{19} + 22 q^{20} - 72 q^{21} + 8 q^{24} + 42 q^{25} - 100 q^{26} + 8 q^{29} - 16 q^{30} - 12 q^{31} - 12 q^{35} - 220 q^{36} - 40 q^{39} - 56 q^{40} + 92 q^{41} + 44 q^{44} - 96 q^{45} + 24 q^{46} + 184 q^{49} - 52 q^{50} + 64 q^{51} + 28 q^{54} + 38 q^{55} - 52 q^{56} + 4 q^{59} + 56 q^{61} + 132 q^{64} + 32 q^{65} - 122 q^{66} - 4 q^{69} + 80 q^{70} - 100 q^{71} - 162 q^{74} + 50 q^{75} - 32 q^{76} - 64 q^{79} - 66 q^{80} - 368 q^{81} - 20 q^{84} - 80 q^{85} - 56 q^{89} - 116 q^{90} - 12 q^{91} - 12 q^{94} - 108 q^{95} + 314 q^{96} + 244 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)