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

• Label: 155.2.e
• Level: $155$
• Weight: $2$
• Character orbit: 155.e
• Rep. character: $\chi_{155}(36,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
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	36	20	16
Cusp forms	28	20	8
Eisenstein series	8	0	8

Trace form

20 * q - 2 * q^3 + 12 * q^4 + 8 * q^6 - 2 * q^7 - 12 * q^8 - 8 * q^9 + 2 * q^10 + 2 * q^11 - 16 * q^12 - 6 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 14 * q^17 - 10 * q^18 + 2 * q^19 + 4 * q^20 + 2 * q^21 + 36 * q^23 + 12 * q^24 - 10 * q^25 - 8 * q^26 - 20 * q^27 + 8 * q^30 + 36 * q^31 - 44 * q^32 - 12 * q^33 + 4 * q^34 + 8 * q^35 + 14 * q^36 + 6 * q^37 + 22 * q^38 - 12 * q^39 - 12 * q^40 - 2 * q^41 + 22 * q^42 - 18 * q^43 - 22 * q^44 - 4 * q^45 - 28 * q^46 - 4 * q^48 - 32 * q^49 - 16 * q^51 - 4 * q^52 - 2 * q^53 + 56 * q^54 - 4 * q^55 - 14 * q^56 + 18 * q^57 + 36 * q^58 - 30 * q^59 - 16 * q^60 - 8 * q^61 - 22 * q^62 + 60 * q^63 - 4 * q^64 - 8 * q^65 - 20 * q^66 - 8 * q^67 + 12 * q^68 - 8 * q^70 - 18 * q^71 + 30 * q^72 + 18 * q^73 + 32 * q^74 - 2 * q^75 - 26 * q^76 + 128 * q^77 - 36 * q^78 + 18 * q^79 + 8 * q^80 + 18 * q^81 - 36 * q^82 - 22 * q^83 + 42 * q^84 - 12 * q^85 - 18 * q^86 + 42 * q^87 - 6 * q^88 + 16 * q^89 + 16 * q^90 + 8 * q^91 + 20 * q^92 + 10 * q^93 + 24 * q^94 + 8 * q^95 - 18 * q^96 - 28 * q^97 - 2 * q^98 - 20 * 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.e.a	$155$	$2$	155.e	31.c	$3$	$2$	$1$	$1.238$	\(\Q(\sqrt{-3}) \)	None		✓			155.2.e.a	$2$	$1$	\(-4\)	\(-2\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{2}+(-2+2\zeta_{6})q^{3}+2q^{4}-\zeta_{6}q^{5}+\cdots\)
155.2.e.b	$155$	$2$	155.e	31.c	$3$	$2$	$1$	$1.238$	\(\Q(\sqrt{-3}) \)	None		✓			155.2.e.b	$2$	$0$	\(4\)	\(-2\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2q^{2}+(-2+2\zeta_{6})q^{3}+2q^{4}+\zeta_{6}q^{5}+\cdots\)
155.2.e.c	$155$	$2$	155.e	31.c	$3$	$8$	$4$	$1.238$	8.0.7007196681.1	None		✓			155.2.e.c	$2$	$0$	\(-2\)	\(3\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{2}+(\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
155.2.e.d	$155$	$2$	155.e	31.c	$3$	$8$	$4$	$1.238$	8.0.42575625.1	None		✓			155.2.e.d	$2$	$0$	\(2\)	\(-1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)

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

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