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

• Label: 155.2.q
• Level: $155$
• Weight: $2$
• Character orbit: 155.q
• Rep. character: $\chi_{155}(41,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.q (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	144	80	64
Cusp forms	112	80	32
Eisenstein series	32	0	32

Trace form

80 * q + 2 * q^3 - 12 * q^4 - 8 * q^6 + 2 * q^7 - 18 * q^8 + 8 * q^9 - 2 * q^10 - 12 * q^11 - 14 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 6 * q^17 + 10 * q^18 - 22 * q^19 - 4 * q^20 - 32 * q^21 - 16 * q^23 + 28 * q^24 - 40 * q^25 + 28 * q^26 - 10 * q^27 + 60 * q^28 + 20 * q^29 + 32 * q^30 - 16 * q^31 - 56 * q^32 + 22 * q^33 + 16 * q^34 + 12 * q^35 - 14 * q^36 - 26 * q^37 - 2 * q^38 - 18 * q^39 + 52 * q^40 + 12 * q^41 - 132 * q^42 - 52 * q^43 - 108 * q^44 + 4 * q^45 - 32 * q^46 + 64 * q^48 + 62 * q^49 - 44 * q^51 + 64 * q^52 + 2 * q^53 + 124 * q^54 - 16 * q^55 + 14 * q^56 + 2 * q^57 - 26 * q^58 + 30 * q^59 + 6 * q^60 - 32 * q^61 + 12 * q^62 + 100 * q^63 - 6 * q^64 + 8 * q^65 - 40 * q^66 + 28 * q^67 - 62 * q^68 - 40 * q^69 + 8 * q^70 - 32 * q^71 + 190 * q^72 + 2 * q^73 + 48 * q^74 + 2 * q^75 + 16 * q^76 - 28 * q^77 - 24 * q^78 - 18 * q^79 - 48 * q^80 - 58 * q^81 - 64 * q^82 - 18 * q^83 + 8 * q^84 + 2 * q^85 + 158 * q^86 - 82 * q^87 - 54 * q^88 + 24 * q^89 - 56 * q^90 - 18 * q^91 + 100 * q^92 - 60 * q^93 + 36 * q^94 - 8 * q^95 + 68 * q^96 + 28 * q^97 - 78 * q^98 + 70 * 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.q.a	$155$	$2$	155.q	31.g	$15$	$40$	$5$	$1.238$		None		✓			155.2.q.a	$2$	$0$	\(-2\)	\(-1\)	\(20\)	\(4\)		$\mathrm{SU}(2)[C_{15}]$
155.2.q.b	$155$	$2$	155.q	31.g	$15$	$40$	$5$	$1.238$		None		✓			155.2.q.b	$2$	$0$	\(2\)	\(3\)	\(-20\)	\(-2\)		$\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(155, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)