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Properties

Label 2368.2.ba
Level $2368$
Weight $2$
Character orbit 2368.ba
Rep. character $\chi_{2368}(417,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 632 152 480
Cusp forms 584 152 432
Eisenstein series 48 0 48

Trace form

\( 152 q + 76 q^{9} + O(q^{10}) \) \( 152 q + 76 q^{9} - 12 q^{17} + 88 q^{25} + 12 q^{41} - 92 q^{49} - 32 q^{57} - 80 q^{73} - 76 q^{81} - 12 q^{89} + 56 q^{97} + O(q^{100}) \)

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

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