Properties

Label 784.4.i
Level $784$
Weight $4$
Character orbit 784.i
Rep. character $\chi_{784}(177,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $116$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 720 124 596
Cusp forms 624 116 508
Eisenstein series 96 8 88

Trace form

\( 116q + 5q^{3} + q^{5} - 485q^{9} + O(q^{10}) \) \( 116q + 5q^{3} + q^{5} - 485q^{9} + 19q^{11} + 4q^{13} + 62q^{15} + q^{17} + 203q^{19} + 121q^{23} - 1165q^{25} - 382q^{27} - 352q^{29} - 307q^{31} - 65q^{33} + 9q^{37} + 734q^{39} - 292q^{41} - 1136q^{43} - 442q^{45} - 573q^{47} - 71q^{51} - 179q^{53} + 58q^{55} + 1802q^{57} + 1405q^{59} + 101q^{61} - 478q^{65} - 1105q^{67} - 3122q^{69} + 1920q^{71} + 1093q^{73} + 780q^{75} - 1183q^{79} - 3378q^{81} - 3848q^{83} + 2334q^{85} - 2350q^{87} + 645q^{89} - 859q^{93} + 1311q^{95} + 2332q^{97} + 8516q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)