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Properties

Label 2368.2.o
Level $2368$
Weight $2$
Character orbit 2368.o
Rep. character $\chi_{2368}(593,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 624 144 480
Cusp forms 592 144 448
Eisenstein series 32 0 32

Trace form

\( 144 q + 16 q^{15} + 16 q^{19} - 24 q^{27} - 24 q^{31} - 24 q^{35} + 32 q^{43} - 144 q^{49} - 16 q^{51} - 8 q^{59} + 32 q^{61} + 24 q^{67} + 32 q^{69} - 32 q^{75} + 8 q^{79} - 144 q^{81} + 40 q^{83} - 32 q^{85}+ \cdots + 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(2368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)