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 - 12 * q^10 + 2 * q^11 - 4 * q^14 + 62 * q^16 + 4 * q^19 - 8 * q^20 + 25 * q^25 + 20 * q^26 + 8 * q^29 - 8 * q^31 - 40 * q^34 + q^35 + 16 * q^40 - 16 * q^41 - 20 * q^44 + 68 * q^46 - 66 * q^49 + 16 * q^50 + 11 * q^55 - 28 * q^56 - 28 * q^59 - 2 * q^61 - 102 * q^64 + 16 * q^65 - 24 * q^70 - 12 * q^71 + 36 * q^74 - 10 * q^76 + 26 * q^80 + 9 * q^85 + 52 * q^86 + 36 * q^89 + 64 * q^91 + 20 * q^94 + q^95

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
855.2.c.a	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None		✓			855.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+(-i-2)q^{5}+2 i q^{7}+\cdots\)
855.2.c.b	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None					95.2.b.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+(2 i+1)q^{5}+2 i q^{7}+\cdots\)
855.2.c.c	$855$	$2$	855.c	5.b	$2$	$2$	$2$	$6.827$	\(\Q(\sqrt{-1}) \)	None		✓			855.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+(-i+2)q^{5}-2 i q^{7}+\cdots\)
855.2.c.d	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.16516096.1	None					95.2.b.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
855.2.c.e	$855$	$2$	855.c	5.b	$2$	$6$	$6$	$6.827$	6.0.350464.1	None					285.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
855.2.c.f	$855$	$2$	855.c	5.b	$2$	$12$	$12$	$6.827$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			855.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{6}q^{7}+\cdots\)
855.2.c.g	$855$	$2$	855.c	5.b	$2$	$14$	$14$	$6.827$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None			✓		285.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(855, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)