Space of modular forms of level 80, weight 11, and Character 80.h

• Label: 80.11.h
• Level: $80$
• Weight: $11$
• Character orbit: 80.h
• Rep. character: $\chi_{80}(79,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $3$
• Sturm bound: $132$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	80.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(80, [\chi])\).

	Total	New	Old
Modular forms	126	30	96
Cusp forms	114	30	84
Eisenstein series	12	0	12

Trace form

30 * q - 4674 * q^5 + 590490 * q^9 - 8860920 * q^21 - 22721682 * q^25 + 58026540 * q^29 + 142012620 * q^41 - 127093926 * q^45 + 2072651370 * q^49 + 2603161500 * q^61 + 2674425408 * q^65 + 1372193160 * q^69 + 24382202790 * q^81 + 22648543104 * q^85 + 5868241500 * q^89

Decomposition of \(S_{11}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.11.h.a	$80$	$11$	80.h	20.d	$2$	$2$	$2$	$50.829$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓	✓			80.11.h.a	$4$	$0$	\(0\)	\(0\)	\(6250\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q-19\beta q^{3}+5^{5}q^{5}-183\beta q^{7}+121451q^{9}+\cdots\)
80.11.h.b	$80$	$11$	80.h	20.d	$2$	$8$	$8$	$50.829$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			80.11.h.b	$4$	$0$	\(0\)	\(0\)	\(-2280\)	\(0\)	$2^{28}\cdot 3^{5}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-285-\beta _{2})q^{5}+(-8\beta _{1}+\cdots)q^{7}+\cdots\)
80.11.h.c	$80$	$11$	80.h	20.d	$2$	$20$	$20$	$50.829$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		80.11.h.c	$4$	$0$	\(0\)	\(0\)	\(-8644\)	\(0\)	$2^{139}\cdot 3^{14}\cdot 5^{12}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{3}+(-432-\beta _{1})q^{5}+(-6\beta _{10}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)