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

• Label: 832.2.i
• Level: $832$
• Weight: $2$
• Character orbit: 832.i
• Rep. character: $\chi_{832}(321,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $52$
• Newform subspaces: $17$
• Sturm bound: $224$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(224\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

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

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

Trace form

\( 52 q + 8 q^{5} - 24 q^{9} + O(q^{10}) \)

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.i.a	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					52.2.e.a	$2$	$0$	\(0\)	\(-3\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
832.2.i.b	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					416.2.i.a	$2$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
832.2.i.c	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					52.2.e.b	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+3q^{5}+4\zeta_{6}q^{7}+\cdots\)
832.2.i.d	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					104.2.i.a	$2$	$1$	\(0\)	\(-1\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.i.e	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					26.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}-4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
832.2.i.f	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					26.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
832.2.i.g	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					104.2.i.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.i.h	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					416.2.i.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
832.2.i.i	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					52.2.e.b	$2$	$0$	\(0\)	\(2\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
832.2.i.j	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	\(\Q(\sqrt{-3}) \)	None					52.2.e.a	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
832.2.i.k	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					416.2.i.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}-2\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
832.2.i.l	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None					104.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
832.2.i.m	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					416.2.i.e	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{3}]$	\(q+(\beta_{3}-2\beta_1-1)q^{5}+(-3\beta_{2}+3)q^{9}+\cdots\)
832.2.i.n	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None					416.2.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+8\beta _{2}q^{9}+\beta _{1}q^{11}+\cdots\)
832.2.i.o	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None					104.2.i.b	$2$	$0$	\(0\)	\(1\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
832.2.i.p	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					416.2.i.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{3}+2\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
832.2.i.q	$832$	$2$	832.i	13.c	$3$	$8$	$4$	$6.644$	8.0.6927565824.3	None			✓		416.2.i.g	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{7})q^{3}+(1-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

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