↑

Properties

Label 2366.2.w
Level $2366$
Weight $2$
Character orbit 2366.w
Rep. character $\chi_{2366}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $408$
Sturm bound $728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 1568 408 1160
Cusp forms 1344 408 936
Eisenstein series 224 0 224

Trace form

\( 408 q + 8 q^{7} - 400 q^{9} + O(q^{10}) \) \( 408 q + 8 q^{7} - 400 q^{9} + 12 q^{11} + 4 q^{12} + 8 q^{14} + 16 q^{15} + 204 q^{16} + 8 q^{18} - 16 q^{19} - 24 q^{21} - 8 q^{22} - 8 q^{28} - 16 q^{29} - 16 q^{31} + 24 q^{33} + 8 q^{35} + 24 q^{36} - 40 q^{37} - 24 q^{41} - 36 q^{42} + 72 q^{43} - 12 q^{46} - 36 q^{47} + 28 q^{49} - 24 q^{51} - 60 q^{55} + 12 q^{56} + 12 q^{57} + 32 q^{58} - 16 q^{60} - 36 q^{62} - 16 q^{63} + 16 q^{67} + 24 q^{68} + 84 q^{69} + 88 q^{70} - 28 q^{71} + 16 q^{72} + 76 q^{73} + 20 q^{74} - 28 q^{75} + 32 q^{76} + 8 q^{79} + 520 q^{81} - 96 q^{82} - 108 q^{83} - 32 q^{84} - 56 q^{85} + 32 q^{86} - 24 q^{87} - 48 q^{89} - 48 q^{92} - 48 q^{93} - 24 q^{95} + 88 q^{97} + 8 q^{98} - 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)