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

• Label: 855.2.dl
• Level: $855$
• Weight: $2$
• Character orbit: 855.dl
• Rep. character: $\chi_{855}(127,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $576$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1536	624	912
Cusp forms	1344	576	768
Eisenstein series	192	48	144

Trace form

576 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 - 60 * q^16 + 30 * q^17 - 36 * q^20 + 24 * q^22 - 24 * q^23 - 36 * q^25 + 72 * q^26 - 36 * q^31 - 6 * q^32 + 30 * q^35 + 78 * q^38 + 54 * q^40 + 60 * q^41 + 24 * q^43 - 36 * q^46 - 126 * q^50 - 6 * q^53 + 18 * q^55 - 168 * q^58 + 108 * q^62 - 72 * q^65 - 84 * q^67 + 30 * q^68 - 60 * q^70 + 24 * q^71 + 6 * q^73 - 180 * q^76 + 48 * q^77 + 36 * q^80 - 84 * q^82 + 12 * q^83 - 84 * q^85 + 84 * q^86 - 198 * q^88 - 24 * q^91 + 120 * q^92 - 24 * q^97 - 102 * 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.dl.a	$855$	$2$	855.dl	95.r	$36$	$96$	$8$	$6.827$		None					95.2.r.a	$4$	$0$	\(12\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
855.2.dl.b	$855$	$2$	855.dl	95.r	$36$	$240$	$20$	$6.827$		None					285.2.bh.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{36}]$
855.2.dl.c	$855$	$2$	855.dl	95.r	$36$	$240$	$20$	$6.827$		None		✓			855.2.dl.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{36}]$

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

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