↑

Properties

Label 1183.2.be
Level $1183$
Weight $2$
Character orbit 1183.be
Rep. character $\chi_{1183}(92,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $1104$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.be (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1183, [\chi])\).

Total New Old
Modular forms 1464 1104 360
Cusp forms 1416 1104 312
Eisenstein series 48 0 48

Trace form

\( 1104 q - 2 q^{2} - 94 q^{4} - 8 q^{5} - 12 q^{6} - 18 q^{8} - 100 q^{9} + O(q^{10}) \) \( 1104 q - 2 q^{2} - 94 q^{4} - 8 q^{5} - 12 q^{6} - 18 q^{8} - 100 q^{9} - 12 q^{10} - 8 q^{11} - 12 q^{12} - 14 q^{13} - 4 q^{14} + 32 q^{15} - 98 q^{16} - 20 q^{17} + 48 q^{18} - 8 q^{19} - 40 q^{20} - 4 q^{21} + 28 q^{22} + 124 q^{23} + 100 q^{24} - 128 q^{25} - 42 q^{26} - 36 q^{27} - 44 q^{29} + 136 q^{30} + 76 q^{31} + 78 q^{32} - 44 q^{33} + 74 q^{34} - 8 q^{35} - 166 q^{36} - 32 q^{37} - 52 q^{38} + 4 q^{39} + 178 q^{40} - 44 q^{41} - 4 q^{42} - 24 q^{43} - 84 q^{44} + 30 q^{45} - 56 q^{46} + 152 q^{47} - 42 q^{48} - 92 q^{49} - 94 q^{50} + 50 q^{51} + 40 q^{52} + 16 q^{53} - 168 q^{54} + 192 q^{55} - 12 q^{56} - 2 q^{57} - 68 q^{58} - 76 q^{59} + 60 q^{60} - 48 q^{61} + 54 q^{62} - 8 q^{63} - 166 q^{64} - 74 q^{65} + 284 q^{66} - 156 q^{68} - 60 q^{69} - 24 q^{70} - 40 q^{71} + 144 q^{72} - 52 q^{73} - 34 q^{74} - 60 q^{75} + 52 q^{76} - 16 q^{77} + 96 q^{78} - 72 q^{79} - 148 q^{80} - 180 q^{81} + 148 q^{82} + 152 q^{83} - 44 q^{84} + 108 q^{85} - 108 q^{86} + 112 q^{87} + 92 q^{88} + 144 q^{89} - 136 q^{90} - 10 q^{91} - 136 q^{92} + 22 q^{93} + 20 q^{94} - 64 q^{95} + 90 q^{96} - 92 q^{97} - 2 q^{98} - 188 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1183, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1183, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)