Properties

Label 468.1.r
Level $468$
Weight $1$
Character orbit 468.r
Rep. character $\chi_{468}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 468.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(468, [\chi])\).

Total New Old
Modular forms 32 4 28
Cusp forms 8 4 4
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4 q - 2 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{7} + 2 q^{13} - 4 q^{25} + 4 q^{31} - 2 q^{43} - 4 q^{55} - 2 q^{61} - 2 q^{67} - 4 q^{73} - 4 q^{79} + 2 q^{91} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(468, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
468.1.r.a 468.r 39.i $4$ $0.234$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(468, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)