Space of modular forms of level 980, weight 2, and Character 980.o

• Label: 980.2.o
• Level: $980$
• Weight: $2$
• Character orbit: 980.o
• Rep. character: $\chi_{980}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Newform subspaces: $7$
• Sturm bound: $336$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(336\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

	Total	New	Old
Modular forms	368	160	208
Cusp forms	304	160	144
Eisenstein series	64	0	64

Trace form

160 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 80 * q^9 + 30 * q^12 + 24 * q^16 - 10 * q^18 - 8 * q^22 - 36 * q^24 + 80 * q^25 - 30 * q^26 + 72 * q^29 - 4 * q^32 - 80 * q^36 - 24 * q^37 + 60 * q^38 + 18 * q^44 - 12 * q^45 + 6 * q^46 - 8 * q^50 + 36 * q^52 + 24 * q^53 - 12 * q^54 - 48 * q^57 + 10 * q^58 - 14 * q^60 - 24 * q^61 - 8 * q^64 - 4 * q^65 - 24 * q^66 - 60 * q^68 + 14 * q^72 + 72 * q^73 - 62 * q^74 - 176 * q^78 - 60 * q^81 - 42 * q^82 + 56 * q^86 - 96 * q^88 + 60 * q^89 - 220 * q^92 + 8 * q^93 - 18 * q^94 + 60 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.2.o.a	$980$	$2$	980.o	28.f	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
980.2.o.b	$980$	$2$	980.o	28.f	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
980.2.o.c	$980$	$2$	980.o	28.f	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
980.2.o.d	$980$	$2$	980.o	28.f	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
980.2.o.e	$980$	$2$	980.o	28.f	$6$	$16$	$8$	$7.825$	16.0.\(\cdots\).8	None					140.2.g.c	$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{8}+\beta _{12}+\beta _{15})q^{3}+\cdots\)
980.2.o.f	$980$	$2$	980.o	28.f	$6$	$32$	$16$	$7.825$		None					140.2.o.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
980.2.o.g	$980$	$2$	980.o	28.f	$6$	$96$	$48$	$7.825$		None		✓	✓		980.2.g.b	$8$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)