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Properties

Label 2365.2.cf
Level $2365$
Weight $2$
Character orbit 2365.cf
Rep. character $\chi_{2365}(16,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $4224$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.cf (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 6432 4224 2208
Cusp forms 6240 4224 2016
Eisenstein series 192 0 192

Trace form

\( 4224 q + 12 q^{2} + 8 q^{3} + 184 q^{4} - 12 q^{6} - 48 q^{7} + 80 q^{8} + 200 q^{9} + O(q^{10}) \) \( 4224 q + 12 q^{2} + 8 q^{3} + 184 q^{4} - 12 q^{6} - 48 q^{7} + 80 q^{8} + 200 q^{9} + 4 q^{11} + 24 q^{12} - 6 q^{13} - 4 q^{14} + 172 q^{16} + 28 q^{17} - 60 q^{18} + 90 q^{19} - 20 q^{20} - 6 q^{22} + 100 q^{23} + 90 q^{24} + 176 q^{25} - 12 q^{26} - 28 q^{27} - 44 q^{28} + 32 q^{29} + 8 q^{30} + 4 q^{31} - 152 q^{32} + 156 q^{33} - 140 q^{34} - 1100 q^{36} + 112 q^{37} + 16 q^{38} + 16 q^{39} + 60 q^{41} + 16 q^{42} - 28 q^{43} + 20 q^{44} - 136 q^{46} - 16 q^{47} + 56 q^{48} - 1040 q^{49} - 16 q^{50} - 72 q^{51} + 16 q^{52} + 124 q^{53} - 24 q^{54} - 32 q^{55} - 100 q^{56} + 60 q^{57} - 88 q^{58} - 80 q^{59} - 42 q^{60} + 16 q^{61} + 32 q^{62} - 156 q^{63} + 400 q^{64} - 64 q^{65} - 226 q^{66} + 108 q^{67} + 462 q^{68} + 76 q^{69} - 20 q^{70} - 124 q^{71} - 180 q^{72} + 104 q^{73} - 70 q^{74} + 30 q^{75} + 152 q^{76} + 52 q^{77} - 244 q^{78} - 240 q^{79} + 16 q^{80} + 454 q^{81} - 92 q^{82} + 34 q^{83} - 116 q^{84} - 48 q^{85} + 258 q^{86} - 320 q^{87} - 382 q^{88} - 40 q^{89} + 32 q^{90} + 48 q^{91} - 208 q^{92} - 220 q^{93} + 392 q^{94} - 366 q^{96} - 122 q^{97} + 16 q^{98} + 88 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)