Space of modular forms of level 4332, weight 2, and trivial character

• Label: 4332.2.a
• Level: $4332$
• Weight: $2$
• Character orbit: 4332.a
• Rep. character: $\chi_{4332}(1,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $21$
• Sturm bound: $1520$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4332.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1520\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4332))\).

	Total	New	Old
Modular forms	820	56	764
Cusp forms	701	56	645
Eisenstein series	119	0	119

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

\(2\)	\(3\)	\(19\)	Fricke	Dim.
\(-\)	\(+\)	\(+\)	\(-\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(15\)
\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(18\)
Plus space			\(+\)	\(25\)
Minus space			\(-\)	\(31\)

Trace form

\( 56 q - 4 q^{5} - 4 q^{7} + 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4332))\) 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	3	19
4332.2.a.a	$4332$	$2$	4332.a	1.a	$1$	$1$	$1$	$34.591$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4332.2.a.b	$4332$	$2$	4332.a	1.a	$1$	$1$	$1$	$34.591$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
4332.2.a.c	$4332$	$2$	4332.a	1.a	$1$	$1$	$1$	$34.591$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4332.2.a.d	$4332$	$2$	4332.a	1.a	$1$	$1$	$1$	$34.591$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
4332.2.a.e	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}-3\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4332.2.a.f	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-2+4\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.g	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4332.2.a.h	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.i	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.j	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}-3\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4332.2.a.k	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(-2+4\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.l	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4332.2.a.m	$4332$	$2$	4332.a	1.a	$1$	$2$	$2$	$34.591$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\)
4332.2.a.n	$4332$	$2$	4332.a	1.a	$1$	$3$	$3$	$34.591$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
4332.2.a.o	$4332$	$2$	4332.a	1.a	$1$	$3$	$3$	$34.591$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
4332.2.a.p	$4332$	$2$	4332.a	1.a	$1$	$4$	$4$	$34.591$	\(\Q(\zeta_{20})^+\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4332.2.a.q	$4332$	$2$	4332.a	1.a	$1$	$4$	$4$	$34.591$	4.4.2225.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
4332.2.a.r	$4332$	$2$	4332.a	1.a	$1$	$4$	$4$	$34.591$	\(\Q(\zeta_{20})^+\)	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4332.2.a.s	$4332$	$2$	4332.a	1.a	$1$	$4$	$4$	$34.591$	4.4.2225.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
4332.2.a.t	$4332$	$2$	4332.a	1.a	$1$	$6$	$6$	$34.591$	6.6.73227321.1	None	✓	$1$	$0$	\(0\)	\(-6\)	\(3\)	\(9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
4332.2.a.u	$4332$	$2$	4332.a	1.a	$1$	$6$	$6$	$34.591$	6.6.73227321.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(3\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 2}\)