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Properties

Label 1840.2.ct
Level $1840$
Weight $2$
Character orbit 1840.ct
Rep. character $\chi_{1840}(17,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1400$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.ct (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 6000 1480 4520
Cusp forms 5520 1400 4120
Eisenstein series 480 80 400

Trace form

\( 1400 q + 18 q^{3} - 22 q^{5} + 22 q^{7} + O(q^{10}) \) \( 1400 q + 18 q^{3} - 22 q^{5} + 22 q^{7} + 44 q^{11} - 18 q^{13} + 22 q^{15} - 22 q^{17} - 44 q^{21} + 32 q^{23} - 18 q^{25} + 54 q^{27} + 20 q^{31} - 22 q^{33} + 18 q^{35} - 22 q^{37} - 52 q^{41} + 22 q^{43} + 64 q^{47} + 44 q^{51} - 22 q^{53} + 86 q^{55} - 22 q^{57} - 44 q^{61} + 22 q^{63} - 22 q^{65} + 22 q^{67} + 36 q^{71} - 18 q^{73} + 126 q^{75} - 46 q^{77} + 56 q^{81} + 22 q^{83} - 18 q^{85} + 78 q^{87} + 4 q^{93} + 214 q^{95} - 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)