Space of modular forms of level 4232, weight 2, and trivial character

• Label: 4232.2.a
• Level: $4232$
• Weight: $2$
• Character orbit: 4232.a
• Rep. character: $\chi_{4232}(1,\cdot)$
• Character field: $\Q$
• Dimension: $126$
• Newform subspaces: $28$
• Sturm bound: $1104$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4232 = 2^{3} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4232.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(1104\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4232))\).

	Total	New	Old
Modular forms	600	126	474
Cusp forms	505	126	379
Eisenstein series	95	0	95

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

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(144\)	\(27\)	\(117\)		\(121\)	\(27\)	\(94\)		\(23\)	\(0\)	\(23\)
\(+\)	\(-\)	\(-\)		\(156\)	\(36\)	\(120\)		\(132\)	\(36\)	\(96\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)		\(156\)	\(33\)	\(123\)		\(132\)	\(33\)	\(99\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)		\(144\)	\(30\)	\(114\)		\(120\)	\(30\)	\(90\)		\(24\)	\(0\)	\(24\)
Plus space		\(+\)		\(288\)	\(57\)	\(231\)		\(241\)	\(57\)	\(184\)		\(47\)	\(0\)	\(47\)
Minus space		\(-\)		\(312\)	\(69\)	\(243\)		\(264\)	\(69\)	\(195\)		\(48\)	\(0\)	\(48\)

Trace form

126 * q + 2 * q^5 + 130 * q^9 - 2 * q^11 - 4 * q^15 + 4 * q^17 - 2 * q^19 + 4 * q^21 + 134 * q^25 - 12 * q^27 - 12 * q^29 + 12 * q^31 + 12 * q^33 + 18 * q^37 + 28 * q^39 - 4 * q^41 + 10 * q^43 - 18 * q^45 + 134 * q^49 - 4 * q^51 + 6 * q^53 - 20 * q^55 + 26 * q^61 + 20 * q^63 - 16 * q^65 - 6 * q^67 + 28 * q^73 + 24 * q^75 - 24 * q^77 - 4 * q^79 + 126 * q^81 - 14 * q^83 - 12 * q^85 - 28 * q^87 - 12 * q^89 + 36 * q^91 - 28 * q^93 + 12 * q^95 + 12 * q^97 - 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4232))\) 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	23
4232.2.a.a	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-2q^{7}-2q^{9}+6q^{11}+\cdots\)
4232.2.a.b	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
4232.2.a.c	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
4232.2.a.d	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}-2q^{9}-6q^{11}+\cdots\)
4232.2.a.e	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓				184.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}-2q^{9}+2q^{11}+\cdots\)
4232.2.a.f	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓				184.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
4232.2.a.g	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓				184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-6q^{11}-2q^{13}-6q^{17}+\cdots\)
4232.2.a.h	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
4232.2.a.i	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓	✓			4232.2.a.h	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
4232.2.a.j	$4232$	$2$	4232.a	1.a	$1$	$1$	$1$	$33.793$	\(\Q\)	None	✓				184.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{7}+6q^{9}-5q^{13}+6q^{17}+\cdots\)
4232.2.a.k	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{2}) \)	None	✓	✓			4232.2.a.k	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}-q^{5}-3\beta q^{7}+(3-4\beta )q^{9}+\cdots\)
4232.2.a.l	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{2}) \)	None	✓	✓			4232.2.a.k	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+q^{5}+3\beta q^{7}+(3-4\beta )q^{9}+\cdots\)
4232.2.a.m	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{3}) \)	None	✓	✓			4232.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-2+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
4232.2.a.n	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{3}) \)	None	✓	✓			4232.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
4232.2.a.o	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{17}) \)	None	✓				184.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
4232.2.a.p	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{6}) \)	None	✓	✓			4232.2.a.p	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-3q^{5}+(2-\beta )q^{7}+3q^{9}-\beta q^{11}+\cdots\)
4232.2.a.q	$4232$	$2$	4232.a	1.a	$1$	$2$	$2$	$33.793$	\(\Q(\sqrt{6}) \)	None	✓	✓			4232.2.a.p	$1$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+3q^{5}+(-2+\beta )q^{7}+3q^{9}+\cdots\)
4232.2.a.r	$4232$	$2$	4232.a	1.a	$1$	$4$	$4$	$33.793$	4.4.9248.1	None	✓	✓			4232.2.a.r	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(2+\cdots)q^{9}+\cdots\)
4232.2.a.s	$4232$	$2$	4232.a	1.a	$1$	$4$	$4$	$33.793$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4232.2.a.s	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-2+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4232.2.a.t	$4232$	$2$	4232.a	1.a	$1$	$4$	$4$	$33.793$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	✓			4232.2.a.t	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+2q^{9}+\cdots\)
4232.2.a.u	$4232$	$2$	4232.a	1.a	$1$	$4$	$4$	$33.793$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4232.2.a.s	$1$	$1$	\(0\)	\(0\)	\(8\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
4232.2.a.v	$4232$	$2$	4232.a	1.a	$1$	$6$	$6$	$33.793$	6.6.26849792.2	None	✓	✓			4232.2.a.v	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(\beta _{3}-\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)
4232.2.a.w	$4232$	$2$	4232.a	1.a	$1$	$8$	$8$	$33.793$	8.8.\(\cdots\).1	None	✓	✓			4232.2.a.w	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{3}+\beta _{1}q^{5}+(-\beta _{3}-\beta _{5})q^{7}+\cdots\)
4232.2.a.x	$4232$	$2$	4232.a	1.a	$1$	$12$	$12$	$33.793$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			4232.2.a.x	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{9}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
4232.2.a.y	$4232$	$2$	4232.a	1.a	$1$	$15$	$15$	$33.793$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		184.2.i.a	$1$	$1$	\(0\)	\(-1\)	\(-10\)	\(-10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{13})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
4232.2.a.z	$4232$	$2$	4232.a	1.a	$1$	$15$	$15$	$33.793$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		184.2.i.a	$1$	$0$	\(0\)	\(-1\)	\(10\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{13})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
4232.2.a.ba	$4232$	$2$	4232.a	1.a	$1$	$15$	$15$	$33.793$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		184.2.i.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}-\beta _{10})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4232.2.a.bb	$4232$	$2$	4232.a	1.a	$1$	$15$	$15$	$33.793$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		184.2.i.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{5}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4232))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4232)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2116))\)\(^{\oplus 2}\)