Space of modular forms of level 855, weight 2, and Character 855.c

• Label: 855.2.c
• Level: $855$
• Weight: $2$
• Character orbit: 855.c
• Rep. character: $\chi_{855}(514,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $7$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).

	Total	New	Old
Modular forms	128	44	84
Cusp forms	112	44	68
Eisenstein series	16	0	16

Trace form

\( 44 q - 42 q^{4} + q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
855.2.c.a	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
855.2.c.b	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(1+2i)q^{5}+2iq^{7}+\cdots\)
855.2.c.c	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(2-i)q^{5}-2iq^{7}+3iq^{8}+\cdots\)
855.2.c.d	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.16516096.1	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
855.2.c.e	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
855.2.c.f	$855$	$2$	855.c	5.b	$2$	$12$	$12$	$6.827$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{6}q^{7}+\cdots\)
855.2.c.g	$855$	$2$	855.c	5.b	$2$	$14$	$14$	$6.827$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \)