Properties

Label 232.2.a
Level $232$
Weight $2$
Character orbit 232.a
Rep. character $\chi_{232}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 232.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(232))\).

Total New Old
Modular forms 34 7 27
Cusp forms 27 7 20
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(29\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(4\)

Trace form

\( 7 q - 4 q^{7} + q^{9} + O(q^{10}) \) \( 7 q - 4 q^{7} + q^{9} - 4 q^{13} - 4 q^{15} - 2 q^{17} + 8 q^{21} - 4 q^{23} + 15 q^{25} + 3 q^{29} - 16 q^{31} + 2 q^{33} + 4 q^{35} + 6 q^{37} + 4 q^{39} - 6 q^{41} - 16 q^{43} + 10 q^{45} - 16 q^{47} - 9 q^{49} + 28 q^{51} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 2 q^{61} - 8 q^{63} - 18 q^{65} + 20 q^{67} - 28 q^{69} + 16 q^{71} + 2 q^{73} + 16 q^{75} + 8 q^{77} - 32 q^{79} - 17 q^{81} - 8 q^{83} - 8 q^{85} + 10 q^{89} - 4 q^{91} - 18 q^{93} + 24 q^{95} - 6 q^{97} + 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(232))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 29
232.2.a.a 232.a 1.a $1$ $1.853$ \(\Q\) None \(0\) \(-1\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
232.2.a.b 232.a 1.a $1$ $1.853$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
232.2.a.c 232.a 1.a $2$ $1.853$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}-4q^{7}+\cdots\)
232.2.a.d 232.a 1.a $3$ $1.853$ 3.3.568.1 None \(0\) \(2\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(232))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(232)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)