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

• Label: 832.2.bu
• Level: $832$
• Weight: $2$
• Character orbit: 832.bu
• Rep. character: $\chi_{832}(63,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $104$
• Newform subspaces: $14$
• Sturm bound: $224$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.bu (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(224\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	496	120	376
Cusp forms	400	104	296
Eisenstein series	96	16	80

Trace form

104 * q + 8 * q^5 + 40 * q^9 + 8 * q^13 - 12 * q^17 + 4 * q^21 + 4 * q^29 - 20 * q^33 + 24 * q^37 - 24 * q^41 - 12 * q^49 + 16 * q^53 - 20 * q^57 + 4 * q^61 - 24 * q^65 + 12 * q^69 - 12 * q^81 + 28 * q^85 - 16 * q^89 + 84 * q^93 - 16 * q^97

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.bu.a	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					208.2.bm.b	$2$	$0$	\(0\)	\(-6\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2+\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{3})q^{5}+\cdots\)
832.2.bu.b	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					416.2.bu.a	$2$	$0$	\(0\)	\(-6\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2+\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
832.2.bu.c	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					208.2.bm.a	$2$	$0$	\(0\)	\(-6\)	\(6\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
832.2.bu.d	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					52.2.l.a	$4$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-2-\zeta_{12}+\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
832.2.bu.e	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					208.2.bm.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(2+3\zeta_{12}-3\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
832.2.bu.f	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					208.2.bm.b	$2$	$0$	\(0\)	\(6\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{3})q^{5}+\cdots\)
832.2.bu.g	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					416.2.bu.a	$2$	$0$	\(0\)	\(6\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
832.2.bu.h	$832$	$2$	832.bu	52.l	$12$	$4$	$1$	$6.644$	\(\Q(\zeta_{12})\)	None					208.2.bm.a	$2$	$0$	\(0\)	\(6\)	\(6\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2+\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
832.2.bu.i	$832$	$2$	832.bu	52.l	$12$	$8$	$2$	$6.644$	8.0.22581504.2	None					416.2.bu.c	$2$	$0$	\(0\)	\(-6\)	\(-4\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\beta _{5})q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
832.2.bu.j	$832$	$2$	832.bu	52.l	$12$	$8$	$2$	$6.644$	8.0.454201344.7	None					208.2.bm.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{3}-2\beta _{4})q^{5}+\cdots\)
832.2.bu.k	$832$	$2$	832.bu	52.l	$12$	$8$	$2$	$6.644$	8.0.22581504.2	None					416.2.bu.c	$2$	$0$	\(0\)	\(6\)	\(-4\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\beta _{5})q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
832.2.bu.l	$832$	$2$	832.bu	52.l	$12$	$16$	$4$	$6.644$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					416.2.bu.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{13})q^{5}+\beta _{12}q^{7}+\cdots\)
832.2.bu.m	$832$	$2$	832.bu	52.l	$12$	$16$	$4$	$6.644$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					416.2.bu.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{4}q^{3}+(-\beta _{11}+\beta _{13})q^{5}-\beta _{12}q^{7}+\cdots\)
832.2.bu.n	$832$	$2$	832.bu	52.l	$12$	$16$	$4$	$6.644$	16.0.\(\cdots\).1	None					52.2.l.b	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{2}-\beta _{14})q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)

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

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