Properties

Label 1840.2.y
Level $1840$
Weight $2$
Character orbit 1840.y
Rep. character $\chi_{1840}(1057,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $140$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 600 148 452
Cusp forms 552 140 412
Eisenstein series 48 8 40

Trace form

\( 140q + 4q^{3} + O(q^{10}) \) \( 140q + 4q^{3} - 4q^{13} - 10q^{23} - 4q^{25} - 32q^{27} + 24q^{31} + 4q^{35} + 8q^{41} - 20q^{47} - 64q^{55} + 8q^{71} - 4q^{73} + 28q^{75} + 24q^{77} - 100q^{81} - 4q^{85} - 56q^{87} - 48q^{93} + 72q^{95} + O(q^{100}) \)

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

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