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

• Label: 80.10.n
• Level: $80$
• Weight: $10$
• Character orbit: 80.n
• Rep. character: $\chi_{80}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $54$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	228	54	174
Cusp forms	204	54	150
Eisenstein series	24	0	24

Trace form

\( 54 q + O(q^{10}) \)

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.n.a	$80$	$10$	80.n	20.e	$4$	$2$	$1$	$41.203$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-1436\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-718-1199i)q^{5}-3^{9}iq^{9}+(29755+\cdots)q^{13}+\cdots\)
80.10.n.b	$80$	$10$	80.n	20.e	$4$	$16$	$8$	$41.203$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(300\)	\(0\)	$2^{44}\cdot 3^{4}\cdot 5^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}+(19-\beta _{1}-393\beta _{3}-\beta _{7}+\cdots)q^{5}+\cdots\)
80.10.n.c	$80$	$10$	80.n	20.e	$4$	$36$	$18$	$41.203$		None		$4$	$0$	\(0\)	\(0\)	\(1136\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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