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Properties

Label 2368.2.br
Level $2368$
Weight $2$
Character orbit 2368.br
Rep. character $\chi_{2368}(433,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $296$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(608\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2368, [\chi])\).

Total New Old
Modular forms 1248 312 936
Cusp forms 1184 296 888
Eisenstein series 64 16 48

Trace form

\( 296 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 296 q + 2 q^{3} - 2 q^{5} + 16 q^{11} - 2 q^{13} + 4 q^{15} - 4 q^{17} + 2 q^{19} - 14 q^{21} + 20 q^{27} - 24 q^{29} + 16 q^{31} - 4 q^{33} + 22 q^{35} + 12 q^{37} + 24 q^{43} - 16 q^{45} - 64 q^{47} + 120 q^{49} - 84 q^{51} - 10 q^{53} + 2 q^{59} - 2 q^{61} + 152 q^{63} + 4 q^{65} - 38 q^{67} + 4 q^{69} + 56 q^{75} + 4 q^{77} + 4 q^{79} + 112 q^{81} + 22 q^{83} + 12 q^{85} + 30 q^{91} - 8 q^{93} - 60 q^{95} - 16 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2368, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)