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

• Label: 855.2.be
• Level: $855$
• Weight: $2$
• Character orbit: 855.be
• Rep. character: $\chi_{855}(64,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.be (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
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	256	104	152
Cusp forms	224	96	128
Eisenstein series	32	8	24

Trace form

96 * q + 42 * q^4 + 2 * q^5 - 2 * q^10 + 16 * q^11 - 14 * q^14 - 34 * q^16 - 14 * q^19 - 4 * q^20 + 4 * q^25 + 4 * q^26 - 14 * q^29 + 6 * q^34 + 14 * q^35 + 10 * q^40 + 4 * q^41 + 68 * q^44 - 24 * q^46 - 88 * q^49 + 56 * q^50 + 16 * q^55 - 116 * q^56 - 38 * q^59 - 24 * q^61 - 40 * q^64 + 20 * q^65 + 6 * q^70 + 48 * q^71 + 42 * q^74 + 22 * q^76 + 10 * q^79 - 20 * q^80 - 38 * q^85 + 56 * q^86 - 30 * q^89 - 40 * q^91 - 84 * q^94 - 28 * 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.be.a	$855$	$2$	855.be	95.i	$6$	$4$	$2$	$6.827$	\(\Q(\zeta_{12})\)	None					95.2.i.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{2}+2\beta_{2} q^{4}+(\beta_{2}-\beta_1-1)q^{5}+\cdots\)
855.2.be.b	$855$	$2$	855.be	95.i	$6$	$8$	$4$	$6.827$	\(\Q(\zeta_{24})\)	None		✓			855.2.be.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{5} q^{2}+(\beta_{5}+\beta_{4}-\beta_{2})q^{5}+(2\beta_{5}-2\beta_{3})q^{8}+\cdots\)
855.2.be.c	$855$	$2$	855.be	95.i	$6$	$8$	$4$	$6.827$	\(\Q(i, \sqrt{3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		✓			855.2.be.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta _{4}+\beta _{5}-\beta _{7})q^{2}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
855.2.be.d	$855$	$2$	855.be	95.i	$6$	$12$	$6$	$6.827$	12.0.\(\cdots\).2	None					95.2.i.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{8}-\beta _{9})q^{4}+\cdots\)
855.2.be.e	$855$	$2$	855.be	95.i	$6$	$24$	$12$	$6.827$		None		✓			855.2.be.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
855.2.be.f	$855$	$2$	855.be	95.i	$6$	$40$	$20$	$6.827$		None			✓		285.2.r.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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