Space of modular forms of level 1632, weight 2, and trivial character

• Label: 1632.2.a
• Level: $1632$
• Weight: $2$
• Character orbit: 1632.a
• Rep. character: $\chi_{1632}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $20$
• Sturm bound: $576$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1632 = 2^{5} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1632.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(576\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1632))\).

	Total	New	Old
Modular forms	304	32	272
Cusp forms	273	32	241
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(6\)
Plus space			\(+\)	\(14\)
Minus space			\(-\)	\(18\)

Trace form

\( 32 q + 32 q^{9} + 16 q^{13} + 16 q^{21} + 16 q^{25} - 16 q^{33} + 16 q^{37} - 32 q^{41} + 16 q^{57} + 16 q^{61} - 32 q^{65} + 32 q^{81} - 64 q^{89} + 16 q^{93} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\) 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	3	17
1632.2.a.a	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
1632.2.a.b	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
1632.2.a.c	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
1632.2.a.d	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-6q^{13}-q^{17}+\cdots\)
1632.2.a.e	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
1632.2.a.f	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
1632.2.a.g	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
1632.2.a.h	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
1632.2.a.i	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
1632.2.a.j	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-6q^{13}-q^{17}+\cdots\)
1632.2.a.k	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.e	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
1632.2.a.l	$1632$	$2$	1632.a	1.a	$1$	$1$	$1$	$13.032$	\(\Q\)	None	✓	✓			1632.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1632.2.a.m	$1632$	$2$	1632.a	1.a	$1$	$2$	$2$	$13.032$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		1632.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
1632.2.a.n	$1632$	$2$	1632.a	1.a	$1$	$2$	$2$	$13.032$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓		1632.2.a.n	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1632.2.a.o	$1632$	$2$	1632.a	1.a	$1$	$2$	$2$	$13.032$	\(\Q(\sqrt{17}) \)	None	✓	✓			1632.2.a.m	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
1632.2.a.p	$1632$	$2$	1632.a	1.a	$1$	$2$	$2$	$13.032$	\(\Q(\sqrt{33}) \)	None	✓	✓			1632.2.a.n	$1$	$0$	\(0\)	\(2\)	\(1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+2q^{7}+q^{9}-\beta q^{11}+\cdots\)
1632.2.a.q	$1632$	$2$	1632.a	1.a	$1$	$3$	$3$	$13.032$	3.3.229.1	None	✓	✓	✓		1632.2.a.q	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-6\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}-2q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
1632.2.a.r	$1632$	$2$	1632.a	1.a	$1$	$3$	$3$	$13.032$	3.3.316.1	None	✓	✓	✓		1632.2.a.r	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
1632.2.a.s	$1632$	$2$	1632.a	1.a	$1$	$3$	$3$	$13.032$	3.3.229.1	None	✓	✓	✓		1632.2.a.q	$1$	$0$	\(0\)	\(3\)	\(1\)	\(6\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+2q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
1632.2.a.t	$1632$	$2$	1632.a	1.a	$1$	$3$	$3$	$13.032$	3.3.316.1	None	✓	✓	✓		1632.2.a.r	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1632))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1632)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)