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Properties

Label 507.4.f
Level $507$
Weight $4$
Character orbit 507.f
Rep. character $\chi_{507}(239,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(507, [\chi])\).

Total New Old
Modular forms 392 328 64
Cusp forms 336 288 48
Eisenstein series 56 40 16

Trace form

\( 288 q + 4 q^{3} - 44 q^{6} - 4 q^{7} + 4 q^{9} + O(q^{10}) \) \( 288 q + 4 q^{3} - 44 q^{6} - 4 q^{7} + 4 q^{9} + 76 q^{15} - 3496 q^{16} - 296 q^{18} - 148 q^{19} + 208 q^{21} + 440 q^{22} - 36 q^{24} + 844 q^{27} - 264 q^{28} + 84 q^{31} - 872 q^{33} - 816 q^{34} + 1440 q^{37} - 4560 q^{40} + 480 q^{42} - 260 q^{45} + 1560 q^{46} + 416 q^{48} + 232 q^{54} + 488 q^{55} - 1028 q^{57} + 1352 q^{58} + 1064 q^{60} - 2056 q^{61} + 652 q^{63} + 9732 q^{66} - 844 q^{67} - 1192 q^{70} - 6984 q^{72} + 416 q^{73} - 2712 q^{76} - 7528 q^{79} - 2492 q^{81} - 5204 q^{84} + 8304 q^{85} - 1880 q^{87} + 4156 q^{93} + 2432 q^{94} + 5956 q^{96} + 5232 q^{97} - 1700 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(507, [\chi]) \cong \)