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Properties

Label 1848.2.dm
Level $1848$
Weight $2$
Character orbit 1848.dm
Rep. character $\chi_{1848}(281,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.dm (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 1600 288 1312
Cusp forms 1472 288 1184
Eisenstein series 128 0 128

Trace form

\( 288 q + 4 q^{3} + 12 q^{9} + O(q^{10}) \) \( 288 q + 4 q^{3} + 12 q^{9} - 12 q^{15} - 60 q^{19} + 60 q^{25} - 8 q^{27} + 16 q^{31} + 18 q^{33} - 8 q^{37} + 60 q^{39} + 24 q^{45} + 72 q^{49} + 70 q^{51} + 8 q^{55} + 30 q^{57} + 40 q^{61} - 72 q^{67} + 60 q^{69} + 40 q^{73} - 10 q^{75} + 40 q^{79} + 52 q^{81} + 60 q^{85} - 16 q^{93} + 108 q^{97} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 2}\)