Properties

Label 2352.4.bo
Level $2352$
Weight $4$
Character orbit 2352.bo
Rep. character $\chi_{2352}(337,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1008$
Sturm bound $1792$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.bo (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

Total New Old
Modular forms 8136 1008 7128
Cusp forms 7992 1008 6984
Eisenstein series 144 0 144

Trace form

\( 1008 q + 6 q^{3} - 18 q^{7} - 1512 q^{9} + O(q^{10}) \) \( 1008 q + 6 q^{3} - 18 q^{7} - 1512 q^{9} - 1548 q^{19} + 168 q^{23} - 4368 q^{25} + 54 q^{27} + 2292 q^{31} + 24 q^{33} - 576 q^{35} + 1050 q^{39} - 592 q^{41} - 84 q^{43} + 408 q^{47} + 280 q^{49} - 784 q^{53} - 3016 q^{55} + 168 q^{57} - 1376 q^{59} - 400 q^{61} + 972 q^{63} + 560 q^{65} + 1092 q^{67} + 560 q^{71} + 768 q^{73} + 1050 q^{75} + 184 q^{77} + 1764 q^{79} - 13608 q^{81} - 4152 q^{83} - 1044 q^{87} + 1712 q^{89} + 6296 q^{91} + 3864 q^{95} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)