Space of modular forms of level 119, weight 2, and trivial character

• Label: 119.2.a
• Level: $119$
• Weight: $2$
• Character orbit: 119.a
• Rep. character: $\chi_{119}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(119))\).

	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.

\(7\)	\(17\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(+\)	\(-\)	\(4\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(9\)

Trace form

9 * q + q^2 + 13 * q^4 + 2 * q^5 - q^7 - 3 * q^8 + 17 * q^9 + 2 * q^10 - 16 * q^12 + 10 * q^13 - 3 * q^14 - 8 * q^15 + 9 * q^16 + q^17 - 19 * q^18 + 16 * q^19 - 22 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^23 - 24 * q^24 + 19 * q^25 - 30 * q^26 - 24 * q^27 - 7 * q^28 - 6 * q^29 - 46 * q^30 + 12 * q^31 - 5 * q^32 + 4 * q^33 + 3 * q^34 + 2 * q^35 + 19 * q^36 + 14 * q^37 - 8 * q^38 - 4 * q^39 + 22 * q^40 + 30 * q^41 + 2 * q^42 - 4 * q^43 + 8 * q^44 - 2 * q^45 + 32 * q^46 - 8 * q^47 - 12 * q^48 + 9 * q^49 + 25 * q^50 - 4 * q^51 + 30 * q^52 - 22 * q^53 + 28 * q^54 - 20 * q^55 - 15 * q^56 + 36 * q^57 - 10 * q^58 + 4 * q^59 + 10 * q^60 + 34 * q^61 + 32 * q^62 - 5 * q^63 + q^64 - 4 * q^65 + 48 * q^66 + 4 * q^67 + 7 * q^68 - 20 * q^69 - 6 * q^70 - 16 * q^71 + 15 * q^72 + 30 * q^73 - 22 * q^74 - 44 * q^75 + 32 * q^76 + 4 * q^77 + 12 * q^78 + 4 * q^79 - 14 * q^80 + 33 * q^81 - 14 * q^82 - 40 * q^83 + 28 * q^84 - 2 * q^85 + 50 * q^86 - 28 * q^87 - 68 * q^88 + 10 * q^89 + 70 * q^90 + 6 * q^91 + 32 * q^92 - 48 * q^93 - 20 * q^94 - 36 * q^95 + 38 * q^97 + q^98 - 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(119))\) 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	17
119.2.a.a	$119$	$2$	119.a	1.a	$1$	$4$	$4$	$0.950$	4.4.9301.1	None	✓	✓	✓	✓	119.2.a.a	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
119.2.a.b	$119$	$2$	119.a	1.a	$1$	$5$	$5$	$0.950$	5.5.453749.1	None	✓	✓	✓	✓	119.2.a.b	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(119))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(119)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)