Space of modular forms of level 6032, weight 2, and trivial character

• Label: 6032.2.a
• Level: $6032$
• Weight: $2$
• Character orbit: 6032.a
• Rep. character: $\chi_{6032}(1,\cdot)$
• Character field: $\Q$
• Dimension: $168$
• Newform subspaces: $31$
• Sturm bound: $1680$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6032.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(1680\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6032))\).

	Total	New	Old
Modular forms	852	168	684
Cusp forms	829	168	661
Eisenstein series	23	0	23

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

\(2\)	\(13\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(19\)
\(+\)	\(+\)	\(-\)	$-$	\(23\)
\(+\)	\(-\)	\(+\)	$-$	\(23\)
\(+\)	\(-\)	\(-\)	$+$	\(19\)
\(-\)	\(+\)	\(+\)	$-$	\(23\)
\(-\)	\(+\)	\(-\)	$+$	\(19\)
\(-\)	\(-\)	\(+\)	$+$	\(19\)
\(-\)	\(-\)	\(-\)	$-$	\(23\)
Plus space			\(+\)	\(76\)
Minus space			\(-\)	\(92\)

Trace form

\( 168 q + 176 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6032))\) 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	13	29
6032.2.a.a	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
6032.2.a.b	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+3q^{7}-2q^{9}+4q^{11}+\cdots\)
6032.2.a.c	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots\)
6032.2.a.d	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}-2q^{9}+q^{13}-3q^{15}+\cdots\)
6032.2.a.e	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}+4q^{11}+q^{13}+2q^{17}+\cdots\)
6032.2.a.f	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
6032.2.a.g	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}-2q^{7}+q^{9}+q^{13}+\cdots\)
6032.2.a.h	$6032$	$2$	6032.a	1.a	$1$	$1$	$1$	$48.166$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+5q^{7}+6q^{9}-4q^{11}+\cdots\)
6032.2.a.i	$6032$	$2$	6032.a	1.a	$1$	$2$	$2$	$48.166$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+2\beta q^{5}+(-3+\beta )q^{7}+\cdots\)
6032.2.a.j	$6032$	$2$	6032.a	1.a	$1$	$2$	$2$	$48.166$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}+(1-\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
6032.2.a.k	$6032$	$2$	6032.a	1.a	$1$	$2$	$2$	$48.166$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta )q^{5}+(-1-2\beta )q^{7}+\cdots\)
6032.2.a.l	$6032$	$2$	6032.a	1.a	$1$	$4$	$4$	$48.166$	4.4.7232.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
6032.2.a.m	$6032$	$2$	6032.a	1.a	$1$	$4$	$4$	$48.166$	4.4.27004.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(7\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
6032.2.a.n	$6032$	$2$	6032.a	1.a	$1$	$5$	$5$	$48.166$	5.5.1220776.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(6\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
6032.2.a.o	$6032$	$2$	6032.a	1.a	$1$	$5$	$5$	$48.166$	5.5.161121.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-6\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}+(-1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
6032.2.a.p	$6032$	$2$	6032.a	1.a	$1$	$5$	$5$	$48.166$	5.5.149169.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
6032.2.a.q	$6032$	$2$	6032.a	1.a	$1$	$5$	$5$	$48.166$	5.5.36497.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{4})q^{3}+(-2\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
6032.2.a.r	$6032$	$2$	6032.a	1.a	$1$	$5$	$5$	$48.166$	5.5.202817.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(15\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{3}+(1+\beta _{3}-\beta _{4})q^{5}+(3+\cdots)q^{7}+\cdots\)
6032.2.a.s	$6032$	$2$	6032.a	1.a	$1$	$6$	$6$	$48.166$	6.6.226964648.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(1-\beta _{5})q^{9}+\cdots\)
6032.2.a.t	$6032$	$2$	6032.a	1.a	$1$	$6$	$6$	$48.166$	6.6.11341289.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
6032.2.a.u	$6032$	$2$	6032.a	1.a	$1$	$7$	$7$	$48.166$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
6032.2.a.v	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(3\)		$+$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{3}q^{7}+(\beta _{3}-\beta _{7}+\cdots)q^{9}+\cdots\)
6032.2.a.w	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.x	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
6032.2.a.y	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-17\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{8}q^{3}+\beta _{3}q^{5}+(-2+\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
6032.2.a.z	$6032$	$2$	6032.a	1.a	$1$	$10$	$10$	$48.166$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(4\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{6}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
6032.2.a.ba	$6032$	$2$	6032.a	1.a	$1$	$10$	$10$	$48.166$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(2\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.bb	$6032$	$2$	6032.a	1.a	$1$	$10$	$10$	$48.166$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.bc	$6032$	$2$	6032.a	1.a	$1$	$11$	$11$	$48.166$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-2\)	\(3\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6032.2.a.bd	$6032$	$2$	6032.a	1.a	$1$	$12$	$12$	$48.166$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(3\)	\(-6\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{6}q^{5}+(-1-\beta _{5}+\cdots)q^{7}+\cdots\)
6032.2.a.be	$6032$	$2$	6032.a	1.a	$1$	$13$	$13$	$48.166$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(5\)	\(-6\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{5}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(377))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(754))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1508))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3016))\)\(^{\oplus 2}\)