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

• Label: 980.2.i
• Level: $980$
• Weight: $2$
• Character orbit: 980.i
• Rep. character: $\chi_{980}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $12$
• Sturm bound: $336$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(336\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	384	28	356
Cusp forms	288	28	260
Eisenstein series	96	0	96

Trace form

28 * q - 2 * q^3 - 2 * q^5 - 10 * q^9 + 6 * q^11 + 8 * q^13 - 8 * q^15 - 4 * q^17 + 8 * q^19 - 6 * q^23 - 14 * q^25 + 28 * q^27 - 16 * q^29 + 4 * q^31 + 12 * q^33 - 12 * q^37 - 10 * q^39 - 4 * q^41 + 60 * q^43 - 4 * q^45 + 8 * q^47 - 14 * q^51 + 24 * q^53 + 8 * q^55 + 24 * q^57 - 8 * q^59 + 6 * q^61 + 6 * q^65 - 46 * q^67 - 60 * q^69 - 16 * q^71 + 4 * q^73 - 2 * q^75 - 26 * q^79 - 6 * q^81 - 4 * q^83 - 20 * q^85 - 6 * q^87 + 10 * q^89 - 40 * q^93 - 12 * q^95 + 40 * q^97 - 120 * q^99

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.i.a	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.i.b	$2$	$0$	\(0\)	\(-3\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.b	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.a.b	$2$	$0$	\(0\)	\(-3\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.c	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					20.2.a.a	$2$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
980.2.i.d	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.e	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None		✓			980.2.a.d	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.f	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.i.a	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
980.2.i.g	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None		✓			980.2.a.d	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.i.h	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.a.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
980.2.i.i	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					20.2.a.a	$2$	$0$	\(0\)	\(2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots\)
980.2.i.j	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	\(\Q(\sqrt{-3}) \)	None					140.2.a.b	$2$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
980.2.i.k	$980$	$2$	980.i	7.c	$3$	$4$	$2$	$7.825$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			980.2.a.j	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
980.2.i.l	$980$	$2$	980.i	7.c	$3$	$4$	$2$	$7.825$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			980.2.a.j	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)