Space of modular forms of level 232, weight 4, and trivial character

• Label: 232.4.a
• Level: $232$
• Weight: $4$
• Character orbit: 232.a
• Rep. character: $\chi_{232}(1,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	232.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(232))\).

	Total	New	Old
Modular forms	94	21	73
Cusp forms	86	21	65
Eisenstein series	8	0	8

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

\(2\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	$+$	\(5\)
Plus space		\(+\)	\(11\)
Minus space		\(-\)	\(10\)

Trace form

\( 21 q + 8 q^{3} - 36 q^{7} + 219 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(232))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	29
232.4.a.a	$232$	$4$	232.a	1.a	$1$	$3$	$3$	$13.688$	3.3.4481.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(11\)	\(-38\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(4+\beta _{1}+\beta _{2})q^{5}+(-13+\cdots)q^{7}+\cdots\)
232.4.a.b	$232$	$4$	232.a	1.a	$1$	$3$	$3$	$13.688$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(4\)	\(16\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-3\beta _{2})q^{3}+(1+3\beta _{1}-4\beta _{2})q^{5}+\cdots\)
232.4.a.c	$232$	$4$	232.a	1.a	$1$	$4$	$4$	$13.688$	4.4.225792.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-20\)	\(-8\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{3}+(-5+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
232.4.a.d	$232$	$4$	232.a	1.a	$1$	$5$	$5$	$13.688$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(10\)	\(32\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{5}+(6+\beta _{2}+\cdots)q^{7}+\cdots\)
232.4.a.e	$232$	$4$	232.a	1.a	$1$	$6$	$6$	$13.688$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-38\)		$-$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(232))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(232)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)