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

• Label: 855.2.bs
• Level: $855$
• Weight: $2$
• Character orbit: 855.bs
• Rep. character: $\chi_{855}(226,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $204$
• Newform subspaces: $8$
• Sturm bound: $240$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(240\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	768	204	564
Cusp forms	672	204	468
Eisenstein series	96	0	96

Trace form

\( 204 q + 6 q^{4} + 18 q^{8} + O(q^{10}) \)

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.bs.a	$855$	$2$	855.bs	19.e	$9$	$12$	$2$	$6.827$	12.0.\(\cdots\).1	None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{8}-\beta _{9})q^{2}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
855.2.bs.b	$855$	$2$	855.bs	19.e	$9$	$18$	$3$	$6.827$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{14}q^{2}+(\beta _{2}+\beta _{4}-\beta _{9}+\beta _{10})q^{4}+\cdots\)
855.2.bs.c	$855$	$2$	855.bs	19.e	$9$	$18$	$3$	$6.827$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{4}-\beta _{15})q^{2}+(\beta _{5}+\beta _{7}+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots\)
855.2.bs.d	$855$	$2$	855.bs	19.e	$9$	$18$	$3$	$6.827$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{5}-\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)
855.2.bs.e	$855$	$2$	855.bs	19.e	$9$	$24$	$4$	$6.827$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$
855.2.bs.f	$855$	$2$	855.bs	19.e	$9$	$30$	$5$	$6.827$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$
855.2.bs.g	$855$	$2$	855.bs	19.e	$9$	$42$	$7$	$6.827$		None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
855.2.bs.h	$855$	$2$	855.bs	19.e	$9$	$42$	$7$	$6.827$		None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)