Space of modular forms of level 882, weight 4, and Character 882.g

• Label: 882.4.g
• Level: $882$
• Weight: $4$
• Character orbit: 882.g
• Rep. character: $\chi_{882}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $100$
• Newform subspaces: $37$
• Sturm bound: $672$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 37 \)
Sturm bound:			\(672\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

	Total	New	Old
Modular forms	1072	100	972
Cusp forms	944	100	844
Eisenstein series	128	0	128

Trace form

\( 100 q - 200 q^{4} + 18 q^{5} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.4.g.a	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-22\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.b	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots\)
882.4.g.c	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots\)
882.4.g.d	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-7\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots\)
882.4.g.e	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.f	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.g	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.h	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.i	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.j	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots\)
882.4.g.k	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots\)
882.4.g.l	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(15\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots\)
882.4.g.m	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(22\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.n	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-22\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.o	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots\)
882.4.g.p	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots\)
882.4.g.q	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.r	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
882.4.g.s	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
882.4.g.t	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.u	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(9\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots\)
882.4.g.v	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots\)
882.4.g.w	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots\)
882.4.g.x	$882$	$4$	882.g	7.c	$3$	$2$	$1$	$52.040$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(22\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.y	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-12\)	\(0\)	$7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.z	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{193})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-7\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.ba	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots\)
882.4.g.bb	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{58})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
882.4.g.bc	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bd	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-4\)	\(0\)	\(12\)	\(0\)	$7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.be	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(4\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bf	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{1345})\)	None		$2$	$0$	\(4\)	\(0\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bg	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bh	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{58})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bi	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bj	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{-3}, \sqrt{193})\)	None		$2$	$0$	\(4\)	\(0\)	\(7\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bk	$882$	$4$	882.g	7.c	$3$	$4$	$2$	$52.040$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(4\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)