Space of modular forms of level 754, weight 2, and trivial character

• Label: 754.2.a
• Level: $754$
• Weight: $2$
• Character orbit: 754.a
• Rep. character: $\chi_{754}(1,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $10$
• Sturm bound: $210$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 754 = 2 \cdot 13 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	754.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(210\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(754))\).

	Total	New	Old
Modular forms	108	27	81
Cusp forms	101	27	74
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.

\(2\)	\(13\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(6\)
Plus space			\(+\)	\(9\)
Minus space			\(-\)	\(18\)

Trace form

\( 27 q + q^{2} + 8 q^{3} + 27 q^{4} + 10 q^{5} + q^{8} + 27 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(754))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	13	29
754.2.a.a	$754$	$2$	754.a	1.a	$1$	$1$	$1$	$6.021$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}+2q^{7}+\cdots\)
754.2.a.b	$754$	$2$	754.a	1.a	$1$	$1$	$1$	$6.021$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
754.2.a.c	$754$	$2$	754.a	1.a	$1$	$1$	$1$	$6.021$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
754.2.a.d	$754$	$2$	754.a	1.a	$1$	$1$	$1$	$6.021$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots\)
754.2.a.e	$754$	$2$	754.a	1.a	$1$	$2$	$2$	$6.021$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2\beta q^{3}+q^{4}+(1-\beta )q^{5}-2\beta q^{6}+\cdots\)
754.2.a.f	$754$	$2$	754.a	1.a	$1$	$2$	$2$	$6.021$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
754.2.a.g	$754$	$2$	754.a	1.a	$1$	$4$	$4$	$6.021$	4.4.27004.1	None	✓	$1$	$0$	\(-4\)	\(0\)	\(7\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
754.2.a.h	$754$	$2$	754.a	1.a	$1$	$4$	$4$	$6.021$	4.4.7232.1	None	✓	$1$	$1$	\(-4\)	\(2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
754.2.a.i	$754$	$2$	754.a	1.a	$1$	$5$	$5$	$6.021$	5.5.1220776.1	None	✓	$1$	$0$	\(5\)	\(3\)	\(6\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
754.2.a.j	$754$	$2$	754.a	1.a	$1$	$6$	$6$	$6.021$	6.6.226964648.1	None	✓	$1$	$0$	\(6\)	\(2\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{4}q^{3}+q^{4}+(1+\beta _{3})q^{5}+\beta _{4}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(754))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(754)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(377))\)\(^{\oplus 2}\)