Properties

Label 2366.2.m
Level $2366$
Weight $2$
Character orbit 2366.m
Rep. character $\chi_{2366}(1037,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 784 152 632
Cusp forms 672 152 520
Eisenstein series 112 0 112

Trace form

\( 152q + 76q^{4} - 76q^{9} + O(q^{10}) \) \( 152q + 76q^{4} - 76q^{9} + 4q^{10} + 12q^{11} - 8q^{14} + 12q^{15} - 76q^{16} + 4q^{17} + 4q^{22} + 4q^{23} - 168q^{25} - 24q^{27} - 16q^{30} - 24q^{33} - 4q^{35} + 76q^{36} - 12q^{37} - 16q^{38} + 8q^{40} + 36q^{41} + 4q^{42} - 8q^{43} - 60q^{45} + 12q^{46} + 76q^{49} + 12q^{50} + 40q^{51} - 48q^{53} + 36q^{54} + 4q^{55} - 4q^{56} - 24q^{58} + 8q^{61} - 12q^{62} + 12q^{63} - 152q^{64} + 48q^{66} + 12q^{67} - 4q^{68} - 4q^{69} + 12q^{72} - 16q^{74} + 40q^{75} + 16q^{79} - 64q^{81} - 12q^{84} - 60q^{85} - 4q^{87} - 4q^{88} - 48q^{90} + 8q^{92} - 48q^{93} - 24q^{94} - 28q^{95} - 48q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)