↑

Properties

Label 1183.2.q
Level $1183$
Weight $2$
Character orbit 1183.q
Rep. character $\chi_{1183}(316,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $156$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 272 156 116
Cusp forms 216 156 60
Eisenstein series 56 0 56

Trace form

\( 156 q + 80 q^{4} + 18 q^{6} - 80 q^{9} + O(q^{10}) \) \( 156 q + 80 q^{4} + 18 q^{6} - 80 q^{9} - 20 q^{10} - 6 q^{11} + 20 q^{12} + 8 q^{14} - 6 q^{15} - 68 q^{16} + 4 q^{17} + 12 q^{20} + 2 q^{22} + 10 q^{23} - 12 q^{24} - 144 q^{25} - 12 q^{27} - 6 q^{29} - 16 q^{30} - 36 q^{32} + 30 q^{33} - 4 q^{35} + 94 q^{36} + 42 q^{37} - 4 q^{38} - 140 q^{40} - 30 q^{41} - 4 q^{42} - 20 q^{43} - 12 q^{46} + 18 q^{48} + 78 q^{49} + 18 q^{50} - 52 q^{51} + 40 q^{53} - 12 q^{54} + 22 q^{55} + 12 q^{56} + 12 q^{58} - 18 q^{59} - 14 q^{61} - 8 q^{62} - 12 q^{63} - 60 q^{64} + 4 q^{66} + 24 q^{67} + 20 q^{68} - 20 q^{69} + 24 q^{71} - 60 q^{72} + 22 q^{74} - 62 q^{75} + 18 q^{76} - 8 q^{77} + 36 q^{79} + 72 q^{80} - 70 q^{81} - 42 q^{82} - 18 q^{84} + 48 q^{85} + 10 q^{87} - 34 q^{88} + 12 q^{89} + 72 q^{90} - 64 q^{92} + 18 q^{93} + 36 q^{94} + 12 q^{95} - 6 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)