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 $728$

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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

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

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

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