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Properties

Label 2368.2.cv
Level $2368$
Weight $2$
Character orbit 2368.cv
Rep. character $\chi_{2368}(383,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $888$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.cv (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 148 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 3792 936 2856
Cusp forms 3504 888 2616
Eisenstein series 288 48 240

Trace form

\( 888 q + 24 q^{5} - 24 q^{9} + O(q^{10}) \) \( 888 q + 24 q^{5} - 24 q^{9} + 24 q^{13} - 24 q^{17} + 24 q^{21} - 48 q^{25} + 24 q^{29} + 12 q^{33} - 24 q^{37} - 24 q^{41} + 24 q^{45} - 24 q^{49} + 24 q^{53} - 24 q^{57} + 24 q^{61} - 48 q^{65} + 24 q^{69} - 108 q^{77} + 12 q^{81} + 36 q^{85} - 24 q^{89} - 120 q^{93} - 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)