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Properties

Label 1232.1.cd
Level $1232$
Weight $1$
Character orbit 1232.cd
Rep. character $\chi_{1232}(97,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1232.cd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1232, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 24 4 20
Eisenstein series 48 8 40

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

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

Trace form

\( 4 q + q^{7} - q^{9} + O(q^{10}) \) \( 4 q + q^{7} - q^{9} + q^{11} + 2 q^{23} - q^{25} - 2 q^{29} + 3 q^{37} + 2 q^{43} - q^{49} + 3 q^{53} + q^{63} + 2 q^{67} - 3 q^{71} - q^{77} - 3 q^{79} - q^{81} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1232.1.cd.a 1232.cd 77.j $4$ $0.615$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\zeta_{10}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)