Space of modular forms of level 832, weight 4, and Character 832.f

• Label: 832.4.f
• Level: $832$
• Weight: $4$
• Character orbit: 832.f
• Rep. character: $\chi_{832}(129,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $14$
• Sturm bound: $448$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	832.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(448\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(832, [\chi])\).

	Total	New	Old
Modular forms	348	86	262
Cusp forms	324	82	242
Eisenstein series	24	4	20

Trace form

\( 82 q + 698 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.4.f.a	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-433}) \)	None		$2$	$0$	\(0\)	\(-14\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-7q^{3}+\beta q^{5}+\beta q^{7}+22q^{9}+(-42+\cdots)q^{13}+\cdots\)
832.4.f.b	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{3}+2\zeta_{6}q^{5}+9\zeta_{6}q^{7}-11q^{9}+\cdots\)
832.4.f.c	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-3iq^{5}-5iq^{7}-26q^{9}-2^{4}iq^{11}+\cdots\)
832.4.f.d	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2iq^{5}-3^{3}q^{9}+(-9+23i)q^{13}+\cdots\)
832.4.f.e	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+3iq^{5}-5iq^{7}-26q^{9}-2^{4}iq^{11}+\cdots\)
832.4.f.f	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{3}-2\zeta_{6}q^{5}+9\zeta_{6}q^{7}-11q^{9}+\cdots\)
832.4.f.g	$832$	$4$	832.f	13.b	$2$	$2$	$2$	$49.090$	\(\Q(\sqrt{-433}) \)	None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+7q^{3}-\beta q^{5}+\beta q^{7}+22q^{9}+(-42+\cdots)q^{13}+\cdots\)
832.4.f.h	$832$	$4$	832.f	13.b	$2$	$4$	$4$	$49.090$	\(\Q(i, \sqrt{217})\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{3}+(\beta _{1}-2\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
832.4.f.i	$832$	$4$	832.f	13.b	$2$	$4$	$4$	$49.090$	\(\Q(i, \sqrt{13})\)	\(\Q(\sqrt{-13}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+(5\beta _{1}-6\beta _{2})q^{7}-3^{3}q^{9}+(7\beta _{1}-13\beta _{2}+\cdots)q^{11}+\cdots\)
832.4.f.j	$832$	$4$	832.f	13.b	$2$	$4$	$4$	$49.090$	\(\Q(i, \sqrt{217})\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{3}+(-\beta _{1}+2\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
832.4.f.k	$832$	$4$	832.f	13.b	$2$	$10$	$10$	$49.090$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{3}+\beta _{8}q^{5}+\beta _{7}q^{7}+(8+\cdots)q^{9}+\cdots\)
832.4.f.l	$832$	$4$	832.f	13.b	$2$	$10$	$10$	$49.090$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{7}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots\)
832.4.f.m	$832$	$4$	832.f	13.b	$2$	$16$	$16$	$49.090$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{12}q^{5}+\beta _{11}q^{7}+(2^{4}+\beta _{2}+\cdots)q^{9}+\cdots\)
832.4.f.n	$832$	$4$	832.f	13.b	$2$	$20$	$20$	$49.090$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{52}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{13}q^{5}-\beta _{18}q^{7}+(14-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(832, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)