Space of modular forms of level 1980, weight 2, and Character 1980.y

• Label: 1980.2.y
• Level: $1980$
• Weight: $2$
• Character orbit: 1980.y
• Rep. character: $\chi_{1980}(1297,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1980.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1980, [\chi])\).

	Total	New	Old
Modular forms	912	60	852
Cusp forms	816	60	756
Eisenstein series	96	0	96

Trace form

\( 60 q - 4 q^{5} - 8 q^{11} - 10 q^{23} + 18 q^{25} + 16 q^{31} + 2 q^{37} - 36 q^{47} + 12 q^{53} + 18 q^{55} - 6 q^{67} + 4 q^{71} + 20 q^{77} + 24 q^{91} + 6 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1980, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1980.2.y.a	$1980$	$2$	1980.y	55.e	$4$	$4$	$2$	$15.810$	\(\Q(i, \sqrt{11})\)	None					220.2.k.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-2\beta _{1})q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots\)
1980.2.y.b	$1980$	$2$	1980.y	55.e	$4$	$8$	$4$	$15.810$	8.0.303595776.1	\(\Q(\sqrt{-11}) \)					220.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\beta _{4}-\beta _{7})q^{11}+\cdots\)
1980.2.y.c	$1980$	$2$	1980.y	55.e	$4$	$24$	$12$	$15.810$		None					660.2.x.a	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1980.2.y.d	$1980$	$2$	1980.y	55.e	$4$	$24$	$12$	$15.810$		None		✓			1980.2.y.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)