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Properties

Label 624.4.r
Level $624$
Weight $4$
Character orbit 624.r
Rep. character $\chi_{624}(499,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $336$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).

Total New Old
Modular forms 680 336 344
Cusp forms 664 336 328
Eisenstein series 16 0 16

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 72 q^{10} - 416 q^{14} + 300 q^{20} - 216 q^{22} + 180 q^{24} - 8400 q^{25} + 368 q^{26} + 344 q^{28} - 140 q^{32} + 1072 q^{34} - 520 q^{38} - 1560 q^{40} - 432 q^{43} + 1332 q^{44} - 400 q^{46} - 3184 q^{50} - 1488 q^{52} + 288 q^{55} - 2600 q^{56} + 1512 q^{58} - 1644 q^{60} - 3192 q^{64} - 1032 q^{68} + 3608 q^{70} + 448 q^{71} - 592 q^{73} + 1104 q^{75} + 7344 q^{76} + 72 q^{78} - 3236 q^{80} - 27216 q^{81} + 7352 q^{82} - 4432 q^{86} + 176 q^{89} - 104 q^{91} - 696 q^{92} - 3848 q^{94} + 2880 q^{96} + 4240 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)