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Properties

Label 2057.4.n
Level $2057$
Weight $4$
Character orbit 2057.n
Rep. character $\chi_{2057}(241,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3824$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2057 = 11^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2057.n (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 4848 3952 896
Cusp forms 4656 3824 832
Eisenstein series 192 128 64

Trace form

\( 3824 q + 16 q^{3} + 16 q^{4} + 16 q^{5} + 16 q^{9} + O(q^{10}) \) \( 3824 q + 16 q^{3} + 16 q^{4} + 16 q^{5} + 16 q^{9} + 128 q^{12} + 336 q^{14} + 16 q^{15} + 16 q^{20} + 352 q^{23} - 880 q^{25} - 1456 q^{26} - 416 q^{27} - 1712 q^{31} - 64 q^{34} - 112 q^{36} + 1360 q^{37} - 640 q^{38} + 3760 q^{42} - 64 q^{45} + 16 q^{47} - 416 q^{48} + 3088 q^{49} + 16 q^{53} - 64 q^{56} + 2592 q^{58} - 304 q^{59} - 5104 q^{60} - 1008 q^{64} - 17440 q^{69} + 19328 q^{70} + 16 q^{71} - 368 q^{75} - 64 q^{78} + 28224 q^{80} - 19776 q^{81} + 16 q^{82} + 5280 q^{86} - 64 q^{89} + 2896 q^{91} - 4464 q^{92} + 3728 q^{93} - 4592 q^{97} + O(q^{100}) \)

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

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