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Properties

Label 507.4.q
Level $507$
Weight $4$
Character orbit 507.q
Rep. character $\chi_{507}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $2160$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.q (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 4416 2160 2256
Cusp forms 4320 2160 2160
Eisenstein series 96 0 96

Trace form

\( 2160 q + 4 q^{2} - 6 q^{3} + 352 q^{4} + 16 q^{5} - 22 q^{7} - 96 q^{8} + 810 q^{9} + O(q^{10}) \) \( 2160 q + 4 q^{2} - 6 q^{3} + 352 q^{4} + 16 q^{5} - 22 q^{7} - 96 q^{8} + 810 q^{9} - 60 q^{10} + 48 q^{11} + 144 q^{12} + 424 q^{13} - 192 q^{14} + 12 q^{15} + 1400 q^{16} + 28 q^{17} - 72 q^{18} + 108 q^{19} - 524 q^{20} - 36 q^{21} + 1312 q^{22} + 24 q^{23} - 180 q^{24} - 3972 q^{25} + 324 q^{26} + 108 q^{27} - 72 q^{28} - 148 q^{29} - 120 q^{30} + 1160 q^{31} + 1358 q^{32} - 96 q^{33} + 1866 q^{34} - 56 q^{35} + 3168 q^{36} + 132 q^{37} - 1262 q^{38} - 264 q^{39} - 1640 q^{40} - 1000 q^{41} - 8652 q^{42} - 246 q^{43} - 280 q^{44} - 72 q^{45} - 28 q^{46} + 1440 q^{47} - 360 q^{48} + 6444 q^{49} + 940 q^{50} + 696 q^{51} - 5894 q^{52} - 2608 q^{53} + 920 q^{55} + 2452 q^{56} + 840 q^{57} + 208 q^{58} - 16404 q^{59} + 48 q^{60} - 982 q^{61} - 5190 q^{62} - 198 q^{63} - 14080 q^{64} - 1124 q^{65} + 360 q^{66} + 4830 q^{67} - 11150 q^{68} - 864 q^{69} + 15848 q^{70} - 11872 q^{71} + 432 q^{72} + 212 q^{73} - 9476 q^{74} - 738 q^{75} - 3212 q^{76} - 3592 q^{77} + 8334 q^{78} + 3276 q^{79} - 1996 q^{80} + 7290 q^{81} + 7614 q^{82} - 1848 q^{83} + 648 q^{84} - 11368 q^{85} - 5928 q^{86} - 6960 q^{87} - 26128 q^{88} + 2312 q^{89} + 1080 q^{90} + 2650 q^{91} - 5040 q^{92} + 20958 q^{93} - 24954 q^{94} + 8724 q^{95} + 5160 q^{96} - 5010 q^{97} - 2680 q^{98} - 864 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(507, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)