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Properties

Label 2057.4.g
Level $2057$
Weight $4$
Character orbit 2057.g
Rep. character $\chi_{2057}(511,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1728$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 2424 1728 696
Cusp forms 2328 1728 600
Eisenstein series 96 0 96

Trace form

\( 1728 q - 4 q^{2} - 8 q^{3} - 1708 q^{4} + 16 q^{5} - 24 q^{6} - 52 q^{7} + 116 q^{8} - 3824 q^{9} + O(q^{10}) \) \( 1728 q - 4 q^{2} - 8 q^{3} - 1708 q^{4} + 16 q^{5} - 24 q^{6} - 52 q^{7} + 116 q^{8} - 3824 q^{9} + 64 q^{10} + 464 q^{12} - 48 q^{13} - 234 q^{14} - 124 q^{15} - 7668 q^{16} - 68 q^{17} + 158 q^{18} + 160 q^{19} + 826 q^{20} - 40 q^{21} + 8 q^{23} - 1024 q^{24} - 11736 q^{25} - 410 q^{26} + 64 q^{27} - 422 q^{28} - 388 q^{29} - 448 q^{30} - 860 q^{31} - 796 q^{32} + 892 q^{35} - 15652 q^{36} - 168 q^{37} - 880 q^{38} - 1084 q^{39} - 380 q^{40} + 484 q^{41} - 1110 q^{42} - 1304 q^{43} + 2456 q^{45} + 3470 q^{46} + 1476 q^{47} + 854 q^{48} - 19636 q^{49} + 1088 q^{50} - 408 q^{51} - 1656 q^{52} - 1516 q^{53} - 7204 q^{54} - 5516 q^{56} - 1144 q^{57} + 322 q^{58} + 1332 q^{59} + 5420 q^{60} + 348 q^{61} + 544 q^{62} + 1108 q^{63} - 32824 q^{64} + 2840 q^{65} - 7208 q^{67} - 816 q^{68} + 1728 q^{69} - 588 q^{70} - 1156 q^{71} - 1858 q^{72} - 3548 q^{73} + 2028 q^{74} + 2032 q^{75} + 1348 q^{76} - 17992 q^{78} - 8 q^{79} - 7440 q^{80} - 33860 q^{81} + 836 q^{82} + 652 q^{83} + 6460 q^{84} + 476 q^{85} + 6604 q^{86} - 2432 q^{87} + 10224 q^{89} + 4496 q^{90} - 3768 q^{91} + 1654 q^{92} + 4108 q^{93} + 448 q^{94} + 964 q^{95} + 7088 q^{96} - 2028 q^{97} + 4616 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(2057, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)