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Properties

Label 507.4.t
Level $507$
Weight $4$
Character orbit 507.t
Rep. character $\chi_{507}(4,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2208$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.t (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 4416 2208 2208
Cusp forms 4320 2208 2112
Eisenstein series 96 0 96

Trace form

\( 2208 q + 6 q^{3} - 376 q^{4} + 18 q^{7} + 828 q^{9} + O(q^{10}) \) \( 2208 q + 6 q^{3} - 376 q^{4} + 18 q^{7} + 828 q^{9} - 8 q^{10} - 24 q^{11} + 144 q^{12} - 338 q^{13} - 224 q^{14} + 36 q^{15} + 1512 q^{16} - 154 q^{17} - 360 q^{19} - 600 q^{20} - 1052 q^{22} + 128 q^{23} + 4972 q^{25} + 744 q^{26} - 108 q^{27} + 588 q^{28} + 278 q^{29} - 120 q^{30} - 1404 q^{31} - 530 q^{32} + 288 q^{33} - 3250 q^{34} - 464 q^{35} - 3384 q^{36} - 282 q^{37} - 1158 q^{38} - 240 q^{39} - 6784 q^{40} - 1182 q^{41} + 8184 q^{42} - 246 q^{43} + 378 q^{45} + 1104 q^{46} + 984 q^{48} - 6842 q^{49} + 3096 q^{50} + 696 q^{51} - 6358 q^{52} - 8078 q^{53} + 7504 q^{55} + 2088 q^{56} + 516 q^{58} + 16316 q^{59} + 2496 q^{60} + 1164 q^{61} - 5658 q^{62} - 162 q^{63} + 11088 q^{64} - 450 q^{65} + 888 q^{66} + 8394 q^{67} + 12710 q^{68} - 240 q^{69} + 11424 q^{71} + 1468 q^{74} - 1362 q^{75} + 4104 q^{76} - 1720 q^{77} + 7242 q^{78} + 676 q^{79} - 8016 q^{80} + 7452 q^{81} + 10318 q^{82} + 2664 q^{84} - 3300 q^{85} - 2184 q^{86} + 7896 q^{87} + 25092 q^{88} - 4416 q^{89} + 144 q^{90} - 7886 q^{91} + 1816 q^{92} - 17346 q^{93} - 6766 q^{94} - 4588 q^{95} - 1242 q^{97} + 6552 q^{98} + O(q^{100}) \)

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

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