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Properties

Label 2368.2.bn
Level $2368$
Weight $2$
Character orbit 2368.bn
Rep. character $\chi_{2368}(399,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $296$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.bn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
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 1248 312 936
Cusp forms 1184 296 888
Eisenstein series 64 16 48

Trace form

\( 296 q + 6 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 296 q + 6 q^{3} - 2 q^{5} + 4 q^{7} + 8 q^{11} - 6 q^{13} - 12 q^{15} - 8 q^{17} + 2 q^{19} - 6 q^{21} - 132 q^{25} - 24 q^{29} - 4 q^{33} - 18 q^{35} + 12 q^{37} + 8 q^{39} - 128 q^{49} + 22 q^{53} + 8 q^{55} + 12 q^{57} + 6 q^{59} - 2 q^{61} - 36 q^{65} + 6 q^{67} - 24 q^{69} + 4 q^{71} - 32 q^{73} - 4 q^{75} + 12 q^{77} + 40 q^{79} + 112 q^{81} + 62 q^{83} + 20 q^{85} - 104 q^{87} - 16 q^{89} + 6 q^{91} + 12 q^{93} - 40 q^{95} - 8 q^{97} + 72 q^{99} + O(q^{100}) \)

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

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