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Properties

Label 2057.4.d
Level $2057$
Weight $4$
Character orbit 2057.d
Rep. character $\chi_{2057}(1937,\cdot)$
Character field $\Q$
Dimension $482$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 606 500 106
Cusp forms 582 482 100
Eisenstein series 24 18 6

Trace form

\( 482 q + 6 q^{2} + 1886 q^{4} + 66 q^{8} - 4190 q^{9} + O(q^{10}) \) \( 482 q + 6 q^{2} + 1886 q^{4} + 66 q^{8} - 4190 q^{9} + 28 q^{13} + 24 q^{15} + 7174 q^{16} - 84 q^{17} - 258 q^{18} + 200 q^{19} - 172 q^{21} - 11334 q^{25} - 368 q^{26} + 4 q^{30} + 614 q^{32} + 656 q^{34} - 240 q^{35} - 15338 q^{36} + 796 q^{38} - 1204 q^{42} + 1088 q^{43} + 780 q^{47} - 21322 q^{49} - 2546 q^{50} + 876 q^{51} + 1116 q^{52} + 452 q^{53} - 320 q^{59} + 1832 q^{60} + 25590 q^{64} + 228 q^{67} - 3334 q^{68} - 1228 q^{69} - 5600 q^{70} - 5750 q^{72} + 5620 q^{76} + 39278 q^{81} + 1352 q^{83} + 420 q^{84} + 2164 q^{85} - 144 q^{86} - 3608 q^{87} - 632 q^{89} - 5228 q^{93} - 5800 q^{94} - 2090 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2057, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)