Properties

Label 1840.4.cv
Level $1840$
Weight $4$
Character orbit 1840.cv
Rep. character $\chi_{1840}(101,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $11520$
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.cv (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 17360 11520 5840
Cusp forms 17200 11520 5680
Eisenstein series 160 0 160

Trace form

\( 11520 q + 40 q^{4} - 60 q^{6} + O(q^{10}) \) \( 11520 q + 40 q^{4} - 60 q^{6} - 120 q^{10} + 80 q^{11} + 156 q^{12} + 280 q^{14} - 240 q^{15} + 864 q^{16} + 360 q^{18} - 48 q^{19} - 472 q^{22} - 456 q^{24} + 264 q^{27} + 760 q^{28} - 800 q^{29} - 3132 q^{34} - 1884 q^{36} - 32 q^{37} + 1980 q^{38} + 1360 q^{42} - 1616 q^{43} - 1000 q^{44} - 13652 q^{46} + 80 q^{48} + 56448 q^{49} + 900 q^{50} - 1488 q^{51} + 1728 q^{52} - 1504 q^{53} + 3888 q^{54} - 1944 q^{56} - 18792 q^{58} + 2040 q^{59} + 1824 q^{61} + 972 q^{62} + 5040 q^{63} - 404 q^{64} + 4400 q^{66} + 4080 q^{67} - 32 q^{68} + 528 q^{69} - 2156 q^{72} - 7656 q^{74} + 2048 q^{76} + 17136 q^{77} - 5548 q^{78} - 5664 q^{79} + 93312 q^{81} + 1404 q^{82} - 7200 q^{84} + 480 q^{85} - 3736 q^{86} + 8040 q^{88} - 2524 q^{92} + 42720 q^{93} - 3992 q^{94} + 12920 q^{96} + 6848 q^{98} + 3600 q^{99} + O(q^{100}) \)

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

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