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

• Label: 855.2.k
• Level: $855$
• Weight: $2$
• Character orbit: 855.k
• Rep. character: $\chi_{855}(406,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $11$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	256	64	192
Cusp forms	224	64	160
Eisenstein series	32	0	32

Trace form

64 * q + 2 * q^2 - 30 * q^4 + 4 * q^7 - 12 * q^8 - 4 * q^10 - 10 * q^13 - 6 * q^14 - 26 * q^16 + 18 * q^17 - 10 * q^19 + 6 * q^22 - 6 * q^23 - 32 * q^25 - 36 * q^26 - 24 * q^28 - 6 * q^29 + 16 * q^31 + 4 * q^32 - 2 * q^34 + 2 * q^35 - 8 * q^37 + 26 * q^38 - 18 * q^40 + 4 * q^41 - 12 * q^43 - 4 * q^44 + 56 * q^46 + 12 * q^47 + 96 * q^49 - 4 * q^50 - 30 * q^52 + 8 * q^53 + 28 * q^56 - 4 * q^58 - 18 * q^59 + 36 * q^61 + 40 * q^62 + 96 * q^64 + 8 * q^65 - 2 * q^67 - 36 * q^68 - 16 * q^70 - 4 * q^71 + 18 * q^73 - 18 * q^74 - 146 * q^76 + 12 * q^77 - 14 * q^79 + 16 * q^80 + 60 * q^82 + 20 * q^83 - 8 * q^85 - 4 * q^86 - 80 * q^88 + 18 * q^89 - 4 * q^91 - 16 * q^92 + 20 * q^94 - 4 * q^95 + 64 * q^97 + 96 * q^98

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.k.a	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	\(\Q(\sqrt{-3}) \)	None					285.2.i.c	$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
855.2.k.b	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	\(\Q(\sqrt{-3}) \)	None					95.2.e.a	$2$	$1$	\(0\)	\(0\)	\(-1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}-4q^{7}-3q^{11}+\cdots\)
855.2.k.c	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	\(\Q(\sqrt{-3}) \)	None					285.2.i.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+2q^{7}+3q^{11}+\cdots\)
855.2.k.d	$855$	$2$	855.k	19.c	$3$	$2$	$1$	$6.827$	\(\Q(\sqrt{-3}) \)	None					285.2.i.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
855.2.k.e	$855$	$2$	855.k	19.c	$3$	$4$	$2$	$6.827$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					285.2.i.e	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
855.2.k.f	$855$	$2$	855.k	19.c	$3$	$4$	$2$	$6.827$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					285.2.i.d	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
855.2.k.g	$855$	$2$	855.k	19.c	$3$	$6$	$3$	$6.827$	6.0.3518667.1	None					95.2.e.b	$2$	$0$	\(1\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{2}-2\beta _{3}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
855.2.k.h	$855$	$2$	855.k	19.c	$3$	$8$	$4$	$6.827$	8.0.4601315889.1	None					95.2.e.c	$2$	$0$	\(1\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{2}+(-1+\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7})q^{4}+\cdots\)
855.2.k.i	$855$	$2$	855.k	19.c	$3$	$10$	$5$	$6.827$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					285.2.i.f	$2$	$0$	\(-1\)	\(0\)	\(5\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{3}-\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
855.2.k.j	$855$	$2$	855.k	19.c	$3$	$12$	$6$	$6.827$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			855.2.k.j	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{9}+\cdots)q^{4}+\cdots\)
855.2.k.k	$855$	$2$	855.k	19.c	$3$	$12$	$6$	$6.827$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			855.2.k.j	$2$	$0$	\(3\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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