Space of modular forms of level 130, weight 2, and trivial character

• Label: 130.2.a
• Level: $130$
• Weight: $2$
• Character orbit: 130.a
• Rep. character: $\chi_{130}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $42$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(42\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(130))\).

	Total	New	Old
Modular forms	24	3	21
Cusp forms	17	3	14
Eisenstein series	7	0	7

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

\(2\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(1\)
Plus space			\(+\)	\(1\)
Minus space			\(-\)	\(2\)

Trace form

3 * q + q^2 + 3 * q^4 + q^5 + 4 * q^6 - 8 * q^7 + q^8 - q^9 - q^10 - 8 * q^11 + q^13 - 4 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 + q^20 + 4 * q^22 + 8 * q^23 + 4 * q^24 + 3 * q^25 - q^26 - 8 * q^28 - 6 * q^29 - 8 * q^31 + q^32 + 8 * q^33 + 10 * q^34 - q^36 + 6 * q^37 - 4 * q^38 - 4 * q^39 - q^40 + 14 * q^41 - 16 * q^42 - 8 * q^43 - 8 * q^44 - 3 * q^45 - 4 * q^46 - 16 * q^47 + 11 * q^49 + q^50 + 16 * q^51 + q^52 + 14 * q^53 - 8 * q^54 - 4 * q^55 + 8 * q^57 + 6 * q^58 + 24 * q^59 - 4 * q^60 + 2 * q^61 - 12 * q^62 - 8 * q^63 + 3 * q^64 + 3 * q^65 - 16 * q^66 - 12 * q^67 - 2 * q^68 + 8 * q^70 - 8 * q^71 - 3 * q^72 + 10 * q^73 + 2 * q^74 + 32 * q^77 - 16 * q^79 + q^80 - 13 * q^81 + 26 * q^82 + 12 * q^83 - 6 * q^85 - 12 * q^86 + 16 * q^87 + 4 * q^88 - 10 * q^89 - 5 * q^90 + 8 * q^92 - 16 * q^93 + 8 * q^94 - 12 * q^95 + 4 * q^96 + 2 * q^97 - 7 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(130))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	13
130.2.a.a	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	\(\Q\)	None	✓	✓	✓	✓	130.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-4q^{7}+\cdots\)
130.2.a.b	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	\(\Q\)	None	✓	✓	✓	✓	130.2.a.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
130.2.a.c	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	\(\Q\)	None	✓	✓	✓	✓	130.2.a.c	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(130))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(130)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)