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		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$	$+$		$36$	$5$	$31$		$33$	$5$	$28$		$3$	$0$	$3$
$+$	$+$	$-$	$-$		$38$	$4$	$34$		$34$	$4$	$30$		$4$	$0$	$4$
$+$	$-$	$+$	$-$		$38$	$5$	$33$		$34$	$5$	$29$		$4$	$0$	$4$
$+$	$-$	$-$	$+$		$36$	$2$	$34$		$32$	$2$	$30$		$4$	$0$	$4$
$-$	$+$	$+$	$-$		$40$	$3$	$37$		$36$	$3$	$33$		$4$	$0$	$4$
$-$	$+$	$-$	$+$		$38$	$4$	$34$		$34$	$4$	$30$		$4$	$0$	$4$
$-$	$-$	$+$	$+$		$38$	$3$	$35$		$34$	$3$	$31$		$4$	$0$	$4$
$-$	$-$	$-$	$-$		$40$	$6$	$34$		$36$	$6$	$30$		$4$	$0$	$4$
Plus space			$+$		$148$	$14$	$134$		$133$	$14$	$119$		$15$	$0$	$15$
Minus space			$-$		$156$	$18$	$138$		$140$	$18$	$122$		$16$	$0$	$16$

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}$