Space of modular forms of level 133, weight 2, and trivial character

• Label: 133.2.a
• Level: $133$
• Weight: $2$
• Character orbit: 133.a
• Rep. character: $\chi_{133}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $26$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(26\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(133))\).

	Total	New	Old
Modular forms	14	9	5
Cusp forms	11	9	2
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.

\(7\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(5\)

Trace form

9 * q - q^2 + 11 * q^4 - 6 * q^5 - q^7 - 9 * q^8 + 9 * q^9 - 10 * q^10 - 8 * q^11 - 16 * q^12 - 6 * q^13 + q^14 + 3 * q^16 - 2 * q^17 + 7 * q^18 + q^19 + 6 * q^20 + 8 * q^22 + 20 * q^24 - q^25 + 2 * q^26 - 12 * q^27 - 7 * q^28 + 2 * q^29 + 12 * q^30 - 8 * q^31 - 9 * q^32 + 36 * q^33 + 18 * q^34 - 2 * q^35 - 5 * q^36 - 22 * q^37 + 3 * q^38 - 20 * q^39 + 6 * q^40 + 10 * q^41 - 12 * q^42 - 20 * q^43 - 8 * q^44 - 18 * q^45 + 24 * q^46 + 12 * q^47 - 36 * q^48 + 9 * q^49 - 7 * q^50 + 36 * q^51 - 14 * q^52 - 10 * q^53 + 16 * q^54 + 12 * q^55 - 3 * q^56 + 10 * q^58 - 36 * q^60 - 6 * q^61 + 4 * q^62 + 3 * q^63 - q^64 + 24 * q^65 - 24 * q^66 + 8 * q^67 - 42 * q^68 + 28 * q^69 + 18 * q^70 + 20 * q^71 - 57 * q^72 - 6 * q^73 + 46 * q^74 - 4 * q^75 + 7 * q^76 - 4 * q^77 - 12 * q^78 - 16 * q^79 + 26 * q^80 + 41 * q^81 + 18 * q^82 + 20 * q^83 + 12 * q^84 + 12 * q^86 + 52 * q^87 + 48 * q^88 - 14 * q^89 - 102 * q^90 - 6 * q^91 + 12 * q^92 - 40 * q^93 - 12 * q^94 - 10 * q^95 + 16 * q^96 - 10 * q^97 - q^98 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(133))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	19
133.2.a.a	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	133.2.a.a	$1$	$1$	\(-3\)	\(-3\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
133.2.a.b	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	133.2.a.b	$1$	$1$	\(-1\)	\(-3\)	\(-6\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-2+\beta )q^{3}+(1+\beta )q^{4}-3q^{5}+\cdots\)
133.2.a.c	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	133.2.a.c	$1$	$0$	\(1\)	\(3\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
133.2.a.d	$133$	$2$	133.a	1.a	$1$	$3$	$3$	$1.062$	3.3.229.1	None	✓	✓	✓	✓	133.2.a.d	$1$	$0$	\(2\)	\(3\)	\(-2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(133))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(133)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)