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Properties

Label 2368.2.bw
Level $2368$
Weight $2$
Character orbit 2368.bw
Rep. character $\chi_{2368}(415,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
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 1264 304 960
Cusp forms 1168 304 864
Eisenstein series 96 0 96

Trace form

\( 304 q + 152 q^{9} + O(q^{10}) \) \( 304 q + 152 q^{9} - 24 q^{17} + 72 q^{25} + 184 q^{49} - 32 q^{57} - 72 q^{65} - 152 q^{81} + 24 q^{89} - 8 q^{97} + O(q^{100}) \)

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

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