Space of modular forms of level 832, weight 2, and trivial character

• Label: 832.2.a
• Level: $832$
• Weight: $2$
• Character orbit: 832.a
• Rep. character: $\chi_{832}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $16$
• Sturm bound: $224$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(224\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(832))\).

	Total	New	Old
Modular forms	124	24	100
Cusp forms	101	24	77
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.

\(2\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(5\)
Plus space		\(+\)	\(10\)
Minus space		\(-\)	\(14\)

Trace form

24 * q + 24 * q^9 + 24 * q^25 - 16 * q^29 - 16 * q^33 - 16 * q^37 - 16 * q^41 + 48 * q^45 + 24 * q^49 + 32 * q^53 - 16 * q^57 - 32 * q^61 + 16 * q^69 + 32 * q^77 - 24 * q^81 + 16 * q^85 - 32 * q^89 + 48 * q^93 - 32 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(832))\) 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	13
832.2.a.a	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				26.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-q^{7}+6q^{9}-2q^{11}+\cdots\)
832.2.a.b	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				416.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
832.2.a.c	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				104.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+5q^{7}-2q^{9}+2q^{11}+\cdots\)
832.2.a.d	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				26.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}-2q^{9}-6q^{11}+\cdots\)
832.2.a.e	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				52.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
832.2.a.f	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				52.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
832.2.a.g	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				416.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
832.2.a.h	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				104.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-5q^{7}-2q^{9}-2q^{11}+\cdots\)
832.2.a.i	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				26.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}-2q^{9}+6q^{11}+\cdots\)
832.2.a.j	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	\(\Q\)	None	✓				26.2.a.b	$1$	$0$	\(0\)	\(3\)	\(1\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+q^{7}+6q^{9}+2q^{11}+\cdots\)
832.2.a.k	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	\(\Q(\sqrt{17}) \)	None	✓		✓		104.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-2+\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.l	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	\(\Q(\sqrt{17}) \)	None	✓				416.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(2-\beta )q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.m	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	\(\Q(\sqrt{5}) \)	None	✓		✓		416.2.a.d	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-3q^{5}+\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots\)
832.2.a.n	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	\(\Q(\sqrt{17}) \)	None	✓				104.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.o	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	\(\Q(\sqrt{17}) \)	None	✓				416.2.a.c	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
832.2.a.p	$832$	$2$	832.a	1.a	$1$	$4$	$4$	$6.644$	4.4.13448.1	None	✓		✓		416.2.a.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(832))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(832)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 2}\)