Space of modular forms of level 155, weight 2, and Character 155.n

• Label: 155.2.n
• Level: $155$
• Weight: $2$
• Character orbit: 155.n
• Rep. character: $\chi_{155}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.n (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9 + 4 * q^10 - 14 * q^11 - 16 * q^14 + 21 * q^15 - 22 * q^16 - 2 * q^19 - 29 * q^20 - 38 * q^21 - 30 * q^24 - 10 * q^25 + 12 * q^26 + 20 * q^29 - 30 * q^30 + 26 * q^31 - 2 * q^34 + 24 * q^35 - 44 * q^36 - 18 * q^39 + 36 * q^40 - 20 * q^41 + 62 * q^44 + 8 * q^45 - 70 * q^46 - 42 * q^49 - 11 * q^50 + 10 * q^51 - 26 * q^54 - 30 * q^55 + 208 * q^56 - 50 * q^59 - 67 * q^60 + 56 * q^61 + 12 * q^64 - 27 * q^65 + 60 * q^66 + 34 * q^69 + 5 * q^70 - 8 * q^71 - 84 * q^74 - 38 * q^75 - 20 * q^76 + 122 * q^79 - 80 * q^80 + 42 * q^81 - 40 * q^84 - 18 * q^85 + 78 * q^86 - 28 * q^89 + 144 * q^90 - 20 * q^91 + 160 * q^94 + 9 * q^95 - 70 * q^96 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.2.n.a	$155$	$2$	155.n	155.n	$10$	$56$	$14$	$1.238$		None		✓	✓	✓	155.2.n.a	$4$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$