Space of modular forms of level 74, weight 2, and trivial character

• Label: 74.2.a
• Level: $74$
• Weight: $2$
• Character orbit: 74.a
• Rep. character: $\chi_{74}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $19$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(19\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(74))\).

	Total	New	Old
Modular forms	11	4	7
Cusp forms	8	4	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.

\(2\)	\(37\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(8\)	\(4\)	\(4\)		\(6\)	\(4\)	\(2\)		\(2\)	\(0\)	\(2\)

Trace form

4 * q + 2 * q^3 + 4 * q^4 - 4 * q^6 + 2 * q^9 + 2 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^14 - 16 * q^15 + 4 * q^16 - 12 * q^17 - 8 * q^18 + 4 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 4 * q^24 + 10 * q^25 + 2 * q^26 + 20 * q^27 + 20 * q^31 - 8 * q^33 + 12 * q^34 - 4 * q^35 + 2 * q^36 - 4 * q^38 + 12 * q^39 + 2 * q^40 + 26 * q^41 + 16 * q^42 - 12 * q^43 - 6 * q^44 - 16 * q^45 + 2 * q^46 + 4 * q^47 + 2 * q^48 + 12 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^53 - 16 * q^54 + 12 * q^55 - 4 * q^56 - 4 * q^57 - 6 * q^58 - 16 * q^60 + 16 * q^61 + 14 * q^62 - 36 * q^63 + 4 * q^64 - 28 * q^65 + 8 * q^66 + 2 * q^67 - 12 * q^68 + 8 * q^69 - 28 * q^70 - 8 * q^72 - 18 * q^73 - 4 * q^74 - 12 * q^75 + 4 * q^76 + 12 * q^77 + 2 * q^78 - 4 * q^79 + 36 * q^81 + 8 * q^82 - 4 * q^84 - 24 * q^85 + 4 * q^87 - 4 * q^88 - 16 * q^89 + 28 * q^90 - 4 * q^92 - 8 * q^93 + 28 * q^95 - 4 * q^96 + 4 * q^97 - 16 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(74))\) 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	37
74.2.a.a	$74$	$2$	74.a	1.a	$1$	$2$	$2$	$0.591$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	74.2.a.a	$1$	$0$	\(-2\)	\(3\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
74.2.a.b	$74$	$2$	74.a	1.a	$1$	$2$	$2$	$0.591$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	74.2.a.b	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(74))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(74)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)