Space of modular forms of level 80, weight 10, and Character 80.c

• Label: 80.10.c
• Level: $80$
• Weight: $10$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(80, [\chi])\).

	Total	New	Old
Modular forms	114	28	86
Cusp forms	102	26	76
Eisenstein series	12	2	10

Trace form

\( 26 q + 358 q^{5} - 157466 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(80, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.10.c.a	$80$	$10$	80.c	5.b	$2$	$4$	$4$	$41.203$	\(\Q(i, \sqrt{319})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2580\)	\(0\)	$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5\beta _{1}-\beta _{3})q^{3}+(-645-54\beta _{1}+\cdots)q^{5}+\cdots\)
80.10.c.b	$80$	$10$	80.c	5.b	$2$	$4$	$4$	$41.203$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(660\)	\(0\)	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(165-\beta _{1}-\beta _{2})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
80.10.c.c	$80$	$10$	80.c	5.b	$2$	$4$	$4$	$41.203$	4.0.49740556.1	None		$2$	$0$	\(0\)	\(0\)	\(1140\)	\(0\)	$2^{7}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(285-7\beta _{1}+7\beta _{2}+\beta _{3})q^{5}+\cdots\)
80.10.c.d	$80$	$10$	80.c	5.b	$2$	$14$	$14$	$41.203$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(1138\)	\(0\)	$2^{101}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(3^{4}-\beta _{2})q^{5}+(-3\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)