Properties

Label 2057.4.m
Level $2057$
Weight $4$
Character orbit 2057.m
Rep. character $\chi_{2057}(188,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $5280$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2057, [\chi])\).

Total New Old
Modular forms 5960 5280 680
Cusp forms 5920 5280 640
Eisenstein series 40 0 40

Trace form

\( 5280 q + 4 q^{2} - 2132 q^{4} + 24 q^{6} + 52 q^{7} - 36 q^{8} + 47520 q^{9} + O(q^{10}) \) \( 5280 q + 4 q^{2} - 2132 q^{4} + 24 q^{6} + 52 q^{7} - 36 q^{8} + 47520 q^{9} + 400 q^{10} + 8 q^{11} + 48 q^{12} - 216 q^{13} - 156 q^{14} - 144 q^{15} - 8452 q^{16} + 68 q^{17} + 292 q^{18} - 160 q^{19} + 380 q^{20} + 40 q^{21} - 402 q^{22} + 1476 q^{23} - 3024 q^{24} - 12792 q^{25} + 180 q^{26} + 312 q^{27} + 92 q^{28} + 988 q^{29} - 32 q^{30} - 552 q^{31} - 984 q^{32} + 316 q^{33} + 408 q^{35} - 20324 q^{36} - 1496 q^{37} - 216 q^{38} + 784 q^{39} - 6340 q^{40} + 1736 q^{41} + 1740 q^{42} - 256 q^{43} + 3456 q^{44} + 392 q^{45} - 880 q^{46} + 256 q^{47} + 1396 q^{48} - 26784 q^{49} + 8082 q^{50} + 408 q^{51} - 1104 q^{52} + 2588 q^{53} - 15520 q^{54} - 2968 q^{55} + 438 q^{56} + 584 q^{57} + 6778 q^{58} + 312 q^{59} + 328 q^{60} + 1452 q^{61} - 624 q^{62} + 9992 q^{63} - 45988 q^{64} - 2056 q^{65} - 792 q^{66} + 2088 q^{67} + 816 q^{68} + 1832 q^{69} + 600 q^{70} + 2568 q^{71} - 2432 q^{72} - 1552 q^{73} - 208 q^{74} + 1120 q^{75} + 24018 q^{76} - 5492 q^{77} - 12324 q^{78} + 1508 q^{79} - 1600 q^{80} + 428616 q^{81} + 8 q^{82} + 2808 q^{83} - 5260 q^{84} - 476 q^{85} + 716 q^{86} - 968 q^{87} + 9314 q^{88} + 10056 q^{89} + 13848 q^{90} - 532 q^{91} - 5496 q^{92} - 592 q^{93} + 2248 q^{94} - 10160 q^{95} - 1088 q^{96} + 4080 q^{97} - 5144 q^{98} + 2840 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2057, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2057, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2057, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)