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Properties

Label 1840.4.x
Level $1840$
Weight $4$
Character orbit 1840.x
Rep. character $\chi_{1840}(461,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1056$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1840, [\chi])\).

Total New Old
Modular forms 1736 1056 680
Cusp forms 1720 1056 664
Eisenstein series 16 0 16

Trace form

\( 1056 q - 60 q^{6} + O(q^{10}) \) \( 1056 q - 60 q^{6} + 156 q^{12} + 208 q^{14} + 280 q^{18} - 80 q^{20} - 1008 q^{22} - 1736 q^{24} - 544 q^{26} + 264 q^{27} - 144 q^{28} + 3200 q^{32} + 1000 q^{34} - 1020 q^{36} - 3160 q^{42} + 4312 q^{44} - 3760 q^{47} - 51744 q^{49} - 2800 q^{51} - 3312 q^{52} - 2528 q^{54} - 3080 q^{56} - 1556 q^{58} + 3416 q^{59} - 1960 q^{60} - 284 q^{62} + 2484 q^{64} - 560 q^{66} + 2480 q^{70} - 324 q^{72} + 3800 q^{74} - 9588 q^{78} - 4640 q^{80} - 85536 q^{81} - 3156 q^{82} - 4880 q^{83} + 5408 q^{84} + 3248 q^{86} + 8600 q^{88} + 4680 q^{90} + 8896 q^{91} - 4272 q^{93} - 9360 q^{94} + 6080 q^{95} - 10760 q^{96} - 3976 q^{98} + 5312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)