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Properties

Label 2057.4.j
Level $2057$
Weight $4$
Character orbit 2057.j
Rep. character $\chi_{2057}(390,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1912$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 2424 1976 448
Cusp forms 2328 1912 416
Eisenstein series 96 64 32

Trace form

\( 1912 q + 2 q^{2} - 1874 q^{4} - 74 q^{8} + 4320 q^{9} + O(q^{10}) \) \( 1912 q + 2 q^{2} - 1874 q^{4} - 74 q^{8} + 4320 q^{9} + 82 q^{13} + 210 q^{15} - 7402 q^{16} + 31 q^{17} + 26 q^{18} + 148 q^{19} - 524 q^{21} + 11004 q^{25} - 354 q^{26} + 648 q^{30} + 2140 q^{32} + 390 q^{34} + 26 q^{35} + 13460 q^{36} - 1380 q^{38} - 1050 q^{42} - 1428 q^{43} + 1422 q^{47} + 20444 q^{49} - 118 q^{50} + 924 q^{51} - 3944 q^{52} - 2838 q^{53} - 2456 q^{59} - 5184 q^{60} - 27854 q^{64} + 9812 q^{67} + 4128 q^{68} + 3732 q^{69} + 5072 q^{70} + 2484 q^{72} + 9144 q^{76} - 29966 q^{81} - 1788 q^{83} - 3176 q^{84} - 4231 q^{85} - 6074 q^{86} + 13900 q^{87} + 4140 q^{89} - 6422 q^{93} + 5428 q^{94} - 11464 q^{98} + O(q^{100}) \)

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

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