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

• Label: 980.2.k
• Level: $980$
• Weight: $2$
• Character orbit: 980.k
• Rep. character: $\chi_{980}(687,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $226$
• Newform subspaces: $13$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	368	266	102
Cusp forms	304	226	78
Eisenstein series	64	40	24

Trace form

226 * q + 2 * q^2 + 4 * q^5 + 8 * q^6 - 16 * q^8 + 10 * q^10 + 16 * q^12 + 6 * q^13 + 16 * q^16 + 14 * q^17 + 2 * q^18 - 16 * q^20 - 16 * q^22 + 14 * q^25 + 28 * q^26 - 16 * q^30 - 28 * q^32 - 36 * q^36 - 6 * q^37 + 40 * q^40 + 16 * q^41 - 26 * q^45 - 40 * q^46 + 24 * q^48 - 18 * q^50 - 12 * q^52 + 26 * q^53 - 24 * q^57 + 20 * q^58 - 60 * q^60 + 40 * q^61 - 40 * q^62 - 22 * q^65 - 32 * q^66 - 68 * q^68 - 84 * q^72 - 30 * q^73 - 8 * q^76 - 32 * q^78 + 4 * q^80 - 18 * q^81 - 72 * q^82 + 14 * q^85 - 32 * q^86 + 64 * q^88 + 10 * q^90 + 44 * q^92 + 24 * q^93 - 120 * q^96 - 46 * q^97

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.k.a	$980$	$2$	980.k	20.e	$4$	$2$	$1$	$7.825$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					20.2.e.a	$4$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}+(-i+2)q^{5}+\cdots\)
980.2.k.b	$980$	$2$	980.k	20.e	$4$	$2$	$1$	$7.825$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.b	$4$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i+1)q^{2}+2 i q^{4}+(-2 i-1)q^{5}+\cdots\)
980.2.k.c	$980$	$2$	980.k	20.e	$4$	$2$	$1$	$7.825$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.b	$4$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i+1)q^{2}+2 i q^{4}+(2 i+1)q^{5}+\cdots\)
980.2.k.d	$980$	$2$	980.k	20.e	$4$	$4$	$2$	$7.825$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.d	$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1+\zeta_{8}^{2})q^{2}-2\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
980.2.k.e	$980$	$2$	980.k	20.e	$4$	$4$	$2$	$7.825$	\(\Q(i, \sqrt{14})\)	None					140.2.w.a	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
980.2.k.f	$980$	$2$	980.k	20.e	$4$	$4$	$2$	$7.825$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.f	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(1-\zeta_{8}^{2})q^{2}-2\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
980.2.k.g	$980$	$2$	980.k	20.e	$4$	$4$	$2$	$7.825$	\(\Q(i, \sqrt{14})\)	None					140.2.w.a	$4$	$0$	\(4\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
980.2.k.h	$980$	$2$	980.k	20.e	$4$	$8$	$4$	$7.825$	\(\Q(\zeta_{24})\)	None		✓			980.2.k.h	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_{6}+\beta_{3})q^{2}+(-\beta_{7}-\beta_{4})q^{3}+\cdots\)
980.2.k.i	$980$	$2$	980.k	20.e	$4$	$32$	$16$	$7.825$		None		✓			980.2.k.i	$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
980.2.k.j	$980$	$2$	980.k	20.e	$4$	$36$	$18$	$7.825$		None					140.2.w.b	$4$	$0$	\(-2\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
980.2.k.k	$980$	$2$	980.k	20.e	$4$	$36$	$18$	$7.825$		None					140.2.w.b	$4$	$0$	\(-2\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
980.2.k.l	$980$	$2$	980.k	20.e	$4$	$36$	$18$	$7.825$		None					140.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
980.2.k.m	$980$	$2$	980.k	20.e	$4$	$56$	$28$	$7.825$		None		✓	✓		980.2.k.m	$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)