Properties

Label 1860.2.ck
Level $1860$
Weight $2$
Character orbit 1860.ck
Rep. character $\chi_{1860}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $128$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1860.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1860, [\chi])\).

Total New Old
Modular forms 1584 128 1456
Cusp forms 1488 128 1360
Eisenstein series 96 0 96

Trace form

\( 128 q - 4 q^{7} + 24 q^{21} + 8 q^{25} - 32 q^{31} + 8 q^{33} - 24 q^{35} - 36 q^{37} + 8 q^{41} - 24 q^{43} - 56 q^{47} + 60 q^{55} - 24 q^{57} - 8 q^{63} + 36 q^{65} - 16 q^{67} - 8 q^{71} + 24 q^{73}+ \cdots + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1860, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1860, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1860, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)