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Properties

Label 2368.2.s
Level $2368$
Weight $2$
Character orbit 2368.s
Rep. character $\chi_{2368}(1807,\cdot)$
Character field $\Q(\zeta_{4})$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(i)\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 624 156 468
Cusp forms 592 148 444
Eisenstein series 32 8 24

Trace form

\( 148 q - 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 148 q - 4 q^{5} + 8 q^{7} - 8 q^{11} + 12 q^{15} - 4 q^{17} + 4 q^{19} + 12 q^{23} + 132 q^{25} + 12 q^{29} - 8 q^{33} + 24 q^{35} + 6 q^{37} + 4 q^{39} + 116 q^{49} - 4 q^{53} + 4 q^{55} - 12 q^{57} - 4 q^{61} + 8 q^{71} - 16 q^{73} + 16 q^{75} - 40 q^{79} - 124 q^{81} + 4 q^{83} - 20 q^{85} - 52 q^{87} - 8 q^{89} + 40 q^{95} - 4 q^{97} + 24 q^{99} + O(q^{100}) \)

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

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