Properties

Label 2304.1.b
Level $2304$
Weight $1$
Character orbit 2304.b
Rep. character $\chi_{2304}(127,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2304.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2304, [\chi])\).

Total New Old
Modular forms 68 4 64
Cusp forms 20 2 18
Eisenstein series 48 2 46

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + 2 q^{25} + 2 q^{49} + 4 q^{73} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2304.1.b.a 2304.b 8.d $2$ $1.150$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) 144.1.g.a \(0\) \(0\) \(0\) \(0\) \(q-2 i q^{13}+q^{25}-2 i q^{37}+q^{49}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)