Properties

Label 6840.2.o
Level $6840$
Weight $2$
Character orbit 6840.o
Rep. character $\chi_{6840}(4751,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $2880$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6840.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(2880\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6840, [\chi])\).

Total New Old
Modular forms 1472 0 1472
Cusp forms 1408 0 1408
Eisenstein series 64 0 64

Decomposition of \(S_{2}^{\mathrm{old}}(6840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3420, [\chi])\)\(^{\oplus 2}\)