Properties

Label 8.21.c
Level 8
Weight 21
Character orbit c
Rep. character \(\chi_{8}(7,\cdot)\)
Character field \(\Q\)
Dimension 0
Newforms 0
Sturm bound 21
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 8.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 0 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(8, [\chi])\).

Total New Old
Modular forms 22 0 22
Cusp forms 18 0 18
Eisenstein series 4 0 4

Decomposition of \(S_{21}^{\mathrm{old}}(8, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(8, [\chi]) \cong \) \(S_{21}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)