Space of modular forms of level 190, weight 2, and trivial character

• Label: 190.2.a
• Level: $190$
• Weight: $2$
• Character orbit: 190.a
• Rep. character: $\chi_{190}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(60\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(190))\).

	Total	New	Old
Modular forms	34	5	29
Cusp forms	27	5	22
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.

\(2\)	\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(7\)	\(0\)	\(7\)		\(6\)	\(0\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(16\)	\(2\)	\(14\)		\(13\)	\(2\)	\(11\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(18\)	\(3\)	\(15\)		\(14\)	\(3\)	\(11\)		\(4\)	\(0\)	\(4\)

Trace form

5 * q - q^2 - 4 * q^3 + 5 * q^4 + q^5 - 8 * q^7 - q^8 + 5 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 + 4 * q^15 + 5 * q^16 - 2 * q^17 + 3 * q^18 - q^19 + q^20 + 24 * q^21 - 12 * q^22 + 8 * q^23 + 5 * q^25 + 2 * q^26 - 16 * q^27 - 8 * q^28 - 10 * q^29 + 4 * q^30 + 8 * q^31 - q^32 + 8 * q^33 - 10 * q^34 + 4 * q^35 + 5 * q^36 - 22 * q^37 + 5 * q^38 - 20 * q^39 - q^40 + 10 * q^41 + 4 * q^42 + 4 * q^44 - 3 * q^45 + 12 * q^46 - 4 * q^47 - 4 * q^48 + q^49 - q^50 + 16 * q^51 - 6 * q^52 - 6 * q^53 - 12 * q^54 + 12 * q^55 - 4 * q^56 - 2 * q^58 - 12 * q^59 + 4 * q^60 + 6 * q^61 - 8 * q^62 - 36 * q^63 + 5 * q^64 + 2 * q^65 + 16 * q^66 - 4 * q^67 - 2 * q^68 - 40 * q^69 + 4 * q^70 + 16 * q^71 + 3 * q^72 - 2 * q^73 - 2 * q^74 - 4 * q^75 - q^76 + 16 * q^77 + 24 * q^78 + q^80 - 3 * q^81 - 10 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 + 2 * q^89 - 13 * q^90 - 16 * q^91 + 8 * q^92 + 16 * q^93 + 4 * q^94 - q^95 - 18 * q^97 + 23 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(190))\) 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	19
190.2.a.a	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	✓	✓	✓	190.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	✓	✓	✓	190.2.a.b	$1$	$1$	\(1\)	\(-3\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	✓	✓	✓	190.2.a.c	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d	$190$	$2$	190.a	1.a	$1$	$2$	$2$	$1.517$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	190.2.a.d	$1$	$0$	\(-2\)	\(-1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(190))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(190)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)