Space of modular forms of level 232, weight 2, and trivial character

• 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: $3$

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.

\(2\)	\(29\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(8\)	\(1\)	\(7\)		\(7\)	\(1\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(9\)	\(3\)	\(6\)		\(7\)	\(3\)	\(4\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(9\)	\(1\)	\(8\)		\(7\)	\(1\)	\(6\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(8\)	\(2\)	\(6\)		\(6\)	\(2\)	\(4\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(16\)	\(3\)	\(13\)		\(13\)	\(3\)	\(10\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(18\)	\(4\)	\(14\)		\(14\)	\(4\)	\(10\)		\(4\)	\(0\)	\(4\)

Trace form

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
232.2.a.a	$232$	$2$	232.a	1.a	$1$	$1$	$1$	$1.853$	\(\Q\)	None	✓	✓	✓	✓	232.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
232.2.a.b	$232$	$2$	232.a	1.a	$1$	$1$	$1$	$1.853$	\(\Q\)	None	✓	✓	✓	✓	232.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
232.2.a.c	$232$	$2$	232.a	1.a	$1$	$2$	$2$	$1.853$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	232.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}-4q^{7}+\cdots\)
232.2.a.d	$232$	$2$	232.a	1.a	$1$	$3$	$3$	$1.853$	3.3.568.1	None	✓	✓	✓	✓	232.2.a.d	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)

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

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