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Properties

Label 2368.2.i
Level $2368$
Weight $2$
Character orbit 2368.i
Rep. character $\chi_{2368}(1025,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $148$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 632 156 476
Cusp forms 584 148 436
Eisenstein series 48 8 40

Trace form

\( 148 q + 2 q^{5} - 72 q^{9} + O(q^{10}) \) \( 148 q + 2 q^{5} - 72 q^{9} - 6 q^{13} + 2 q^{17} - 18 q^{21} - 64 q^{25} - 8 q^{29} - 8 q^{33} + 4 q^{37} + 2 q^{41} + 24 q^{45} - 64 q^{49} - 14 q^{53} + 10 q^{57} + 18 q^{61} + 18 q^{65} + 56 q^{69} - 24 q^{73} + 24 q^{77} - 66 q^{81} - 12 q^{85} - 6 q^{89} - 24 q^{93} - 16 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)