Space of modular forms of level 155, weight 2, and trivial character

• Label: 155.2.a
• Level: $155$
• Weight: $2$
• Character orbit: 155.a
• Rep. character: $\chi_{155}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(155))\).

	Total	New	Old
Modular forms	18	11	7
Cusp forms	15	11	4
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)	\(31\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(8\)	\(5\)	\(3\)		\(7\)	\(5\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(5\)	\(4\)	\(1\)		\(4\)	\(4\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(13\)	\(9\)	\(4\)		\(11\)	\(9\)	\(2\)		\(2\)	\(0\)	\(2\)

Trace form

11 * q - 3 * q^2 + 13 * q^4 - q^5 + 4 * q^6 + 4 * q^7 - 3 * q^8 + 3 * q^9 + q^10 - 8 * q^11 - 4 * q^12 + 14 * q^13 - 8 * q^14 + 13 * q^16 + 2 * q^17 - 11 * q^18 + q^20 + 12 * q^21 - 24 * q^22 + 12 * q^23 - 24 * q^24 + 11 * q^25 + 2 * q^26 + 12 * q^27 - 16 * q^28 - 18 * q^29 - 8 * q^30 + q^31 - 19 * q^32 - 12 * q^33 + 2 * q^34 - 4 * q^35 - 31 * q^36 + 2 * q^37 - 16 * q^38 - 4 * q^39 + 9 * q^40 - 10 * q^41 - 28 * q^42 + 20 * q^43 + 4 * q^44 - 9 * q^45 - 20 * q^46 - 24 * q^47 - 16 * q^48 + 11 * q^49 - 3 * q^50 - 8 * q^51 + 42 * q^52 + 26 * q^53 + 28 * q^54 + 4 * q^55 - 16 * q^56 + 8 * q^57 + 18 * q^58 + 12 * q^59 + 12 * q^60 + 34 * q^61 - 5 * q^62 - 16 * q^63 + 29 * q^64 - 6 * q^65 + 8 * q^66 - 8 * q^67 + 42 * q^68 + 12 * q^69 - 16 * q^70 - 12 * q^71 + 9 * q^72 + 14 * q^73 - 2 * q^74 + 4 * q^76 + 28 * q^77 + 24 * q^78 - 28 * q^79 - 15 * q^80 + 7 * q^81 + 54 * q^82 - 32 * q^83 + 32 * q^84 + 6 * q^85 + 12 * q^86 + 12 * q^87 - 36 * q^88 + 2 * q^89 - 7 * q^90 - 16 * q^91 + 4 * q^92 + 24 * q^94 - 16 * q^95 + 24 * q^96 + 6 * q^97 + 53 * q^98 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(155))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	31
155.2.a.a	$155$	$2$	155.a	1.a	$1$	$1$	$1$	$1.238$	\(\Q\)	None	✓	✓	✓	✓	155.2.a.a	$1$	$1$	\(-2\)	\(-1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
155.2.a.b	$155$	$2$	155.a	1.a	$1$	$1$	$1$	$1.238$	\(\Q\)	None	✓	✓			155.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(-1\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
155.2.a.c	$155$	$2$	155.a	1.a	$1$	$1$	$1$	$1.238$	\(\Q\)	None	✓	✓	✓	✓	155.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-2q^{9}-4q^{11}+\cdots\)
155.2.a.d	$155$	$2$	155.a	1.a	$1$	$4$	$4$	$1.238$	4.4.20308.1	None	✓	✓	✓		155.2.a.d	$1$	$0$	\(-1\)	\(-1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
155.2.a.e	$155$	$2$	155.a	1.a	$1$	$4$	$4$	$1.238$	4.4.8468.1	None	✓	✓	✓	✓	155.2.a.e	$1$	$0$	\(1\)	\(1\)	\(4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(155)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)