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Properties

Label 2368.2.db
Level $2368$
Weight $2$
Character orbit 2368.db
Rep. character $\chi_{2368}(79,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $888$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.db (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 3744 936 2808
Cusp forms 3552 888 2664
Eisenstein series 192 48 144

Trace form

\( 888 q + 12 q^{3} - 12 q^{5} + 24 q^{7} + O(q^{10}) \) \( 888 q + 12 q^{3} - 12 q^{5} + 24 q^{7} + 18 q^{11} - 12 q^{13} - 24 q^{17} + 12 q^{19} - 12 q^{21} + 24 q^{23} + 18 q^{27} - 18 q^{29} - 24 q^{33} + 12 q^{35} - 60 q^{37} + 24 q^{39} - 6 q^{45} - 24 q^{49} - 54 q^{51} + 12 q^{53} + 24 q^{55} + 12 q^{59} - 12 q^{61} + 12 q^{67} - 30 q^{69} + 24 q^{71} - 48 q^{73} + 24 q^{75} - 30 q^{77} - 24 q^{81} + 72 q^{83} - 18 q^{85} + 192 q^{87} + 48 q^{89} + 12 q^{91} - 48 q^{93} - 24 q^{97} - 294 q^{99} + O(q^{100}) \)

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

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