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Properties

Label 2904.1.bh
Level $2904$
Weight $1$
Character orbit 2904.bh
Rep. character $\chi_{2904}(131,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $20$
Newform subspaces $2$
Sturm bound $528$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2904.bh (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2904 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(528\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2904, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + 2 q^{3} - 2 q^{4} - 2 q^{9} - 9 q^{12} - 2 q^{16} + 2 q^{22} + 2 q^{25} + 2 q^{27} + 4 q^{34} - 2 q^{36} + 2 q^{48} + 2 q^{49} - 11 q^{51} + 11 q^{57} - 2 q^{64} + 9 q^{66} - 4 q^{67} - 2 q^{75}+ \cdots + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2904, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2904.1.bh.a 2904.bh 2904.ah $10$ $1.449$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-2}) \) None 2904.1.bh.a \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{22}^{10}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}^{9}q^{4}+\cdots\)
2904.1.bh.b 2904.bh 2904.ah $10$ $1.449$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-2}) \) None 2904.1.bh.a \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{22}^{10}q^{2}-\zeta_{22}^{2}q^{3}-\zeta_{22}^{9}q^{4}+\cdots\)