Space of modular forms of level 832, weight 2, and Character 832.k

• Label: 832.2.k
• Level: $832$
• Weight: $2$
• Character orbit: 832.k
• Rep. character: $\chi_{832}(255,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $52$
• Newform subspaces: $10$
• Sturm bound: $224$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(224\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(832, [\chi])\).

	Total	New	Old
Modular forms	248	60	188
Cusp forms	200	52	148
Eisenstein series	48	8	40

Trace form

\( 52 q + 4 q^{5} - 52 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(832, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.2.k.a	$832$	$2$	832.k	52.f	$4$	$2$	$1$	$6.644$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					208.2.k.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{5}+3 q^{9}+(-3 i-2)q^{13}+\cdots\)
832.2.k.b	$832$	$2$	832.k	52.f	$4$	$2$	$1$	$6.644$	\(\Q(\sqrt{-1}) \)	None					416.2.k.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2 i q^{3}+(i+1)q^{5}+(-i-1)q^{7}+\cdots\)
832.2.k.c	$832$	$2$	832.k	52.f	$4$	$2$	$1$	$6.644$	\(\Q(\sqrt{-1}) \)	None					416.2.k.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-2 i q^{3}+(i+1)q^{5}+(i+1)q^{7}+\cdots\)
832.2.k.d	$832$	$2$	832.k	52.f	$4$	$2$	$1$	$6.644$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					52.2.f.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(3 i+3)q^{5}+3 q^{9}+(-3 i+2)q^{13}+\cdots\)
832.2.k.e	$832$	$2$	832.k	52.f	$4$	$4$	$2$	$6.644$	\(\Q(i, \sqrt{10})\)	None					416.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
832.2.k.f	$832$	$2$	832.k	52.f	$4$	$4$	$2$	$6.644$	\(\Q(i, \sqrt{10})\)	None					416.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(1+\cdots)q^{11}+\cdots\)
832.2.k.g	$832$	$2$	832.k	52.f	$4$	$8$	$4$	$6.644$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					416.2.k.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{2}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
832.2.k.h	$832$	$2$	832.k	52.f	$4$	$8$	$4$	$6.644$	8.0.18939904.2	None					52.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots\)
832.2.k.i	$832$	$2$	832.k	52.f	$4$	$8$	$4$	$6.644$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					416.2.k.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots\)
832.2.k.j	$832$	$2$	832.k	52.f	$4$	$12$	$6$	$6.644$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		208.2.k.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}-\beta _{5}q^{5}+\beta _{10}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)