Space of modular forms of level 145, weight 2, and trivial character

• Label: 145.2.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.a
• Rep. character: $\chi_{145}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(145))\).

	Total	New	Old
Modular forms	16	9	7
Cusp forms	13	9	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.

\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(6\)	\(3\)	\(3\)		\(5\)	\(3\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(6\)	\(3\)	\(3\)		\(5\)	\(3\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(10\)	\(6\)	\(4\)		\(8\)	\(6\)	\(2\)		\(2\)	\(0\)	\(2\)

Trace form

9 * q + q^2 - 4 * q^3 + 7 * q^4 + q^5 + 4 * q^6 - 4 * q^7 + 9 * q^8 + 5 * q^9 - 3 * q^10 - 16 * q^12 - 10 * q^13 - 8 * q^14 + 7 * q^16 - 6 * q^17 - 7 * q^18 - 16 * q^19 - q^20 + 12 * q^22 + 20 * q^23 - 12 * q^24 + 9 * q^25 - 2 * q^26 + 8 * q^27 + 4 * q^28 + q^29 - 4 * q^30 - 4 * q^31 + 9 * q^32 - 8 * q^33 - 18 * q^34 + 4 * q^35 - 21 * q^36 + 6 * q^37 - 12 * q^38 + 32 * q^39 - 15 * q^40 - 22 * q^41 + 8 * q^42 - 12 * q^43 + 5 * q^45 + 40 * q^46 + 8 * q^47 - 12 * q^48 + q^49 + q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 24 * q^54 - 4 * q^55 - 24 * q^56 - 8 * q^57 + q^58 + 4 * q^59 - 12 * q^60 - 2 * q^61 + 40 * q^62 + 12 * q^63 + 15 * q^64 - 2 * q^65 - 16 * q^66 + 16 * q^67 - 38 * q^68 + 16 * q^69 + 12 * q^70 + 32 * q^71 - 31 * q^72 - 26 * q^73 - 46 * q^74 - 4 * q^75 + 16 * q^76 + 4 * q^77 - 24 * q^78 + 4 * q^79 - q^80 - 15 * q^81 + 26 * q^82 + 16 * q^83 - 16 * q^84 - 2 * q^85 + 12 * q^86 - 8 * q^87 + 52 * q^88 + 26 * q^89 + 13 * q^90 - 24 * q^91 - 4 * q^92 + 8 * q^94 - 12 * q^95 + 4 * q^96 - 34 * q^97 + 69 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(145))\) 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	29
145.2.a.a	$145$	$2$	145.a	1.a	$1$	$1$	$1$	$1.158$	\(\Q\)	None	✓	✓	✓	✓	145.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots\)
145.2.a.b	$145$	$2$	145.a	1.a	$1$	$2$	$2$	$1.158$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	145.2.a.b	$1$	$1$	\(-2\)	\(-4\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
145.2.a.c	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	None	✓	✓	✓	✓	145.2.a.c	$1$	$0$	\(1\)	\(2\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
145.2.a.d	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	None	✓	✓	✓	✓	145.2.a.d	$1$	$0$	\(3\)	\(-2\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(145)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)