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

• Label: 855.2.n
• Level: $855$
• Weight: $2$
• Character orbit: 855.n
• Rep. character: $\chi_{855}(647,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(7\)
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	72	184
Cusp forms	224	72	152
Eisenstein series	32	0	32

Trace form

72 * q + 16 * q^7 + 16 * q^10 + 8 * q^13 - 72 * q^16 - 48 * q^22 - 16 * q^28 - 32 * q^31 + 24 * q^37 + 24 * q^40 + 56 * q^43 + 32 * q^46 - 72 * q^52 + 16 * q^55 + 72 * q^58 + 32 * q^61 + 64 * q^67 - 128 * q^70 - 80 * q^73 + 56 * q^82 + 64 * q^85 - 144 * q^88 - 32 * q^91 + 56 * q^97

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.n.a	$855$	$2$	855.n	15.e	$4$	$4$	$2$	$6.827$	\(\Q(\zeta_{8})\)	None		✓			855.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
855.2.n.b	$855$	$2$	855.n	15.e	$4$	$4$	$2$	$6.827$	\(\Q(\zeta_{8})\)	None		✓			855.2.n.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
855.2.n.c	$855$	$2$	855.n	15.e	$4$	$8$	$4$	$6.827$	\(\Q(\zeta_{24})\)	None		✓			855.2.n.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{24}-2\zeta_{24}^{5})q^{2}-2\zeta_{24}^{6}q^{4}+\cdots\)
855.2.n.d	$855$	$2$	855.n	15.e	$4$	$20$	$10$	$6.827$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			855.2.n.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{10})q^{4}+(\beta _{1}-\beta _{16}+\cdots)q^{5}+\cdots\)
855.2.n.e	$855$	$2$	855.n	15.e	$4$	$36$	$18$	$6.827$		None		✓	✓		855.2.n.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

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

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