Space of modular forms of level 799, weight 2, and trivial character

• Label: 799.2.a
• Level: $799$
• Weight: $2$
• Character orbit: 799.a
• Rep. character: $\chi_{799}(1,\cdot)$
• Character field: $\Q$
• Dimension: $61$
• Newform subspaces: $7$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(799))\).

	Total	New	Old
Modular forms	74	61	13
Cusp forms	71	61	10
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.

\(17\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	$-$	\(20\)
\(-\)	\(+\)	$-$	\(18\)
\(-\)	\(-\)	$+$	\(11\)
Plus space		\(+\)	\(23\)
Minus space		\(-\)	\(38\)

Trace form

\( 61 q - q^{2} + 59 q^{4} + 6 q^{5} + 8 q^{6} - 16 q^{7} + 3 q^{8} + 69 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(799))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17	47
799.2.a.a	$799$	$2$	799.a	1.a	$1$	$1$	$1$	$6.380$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots\)
799.2.a.b	$799$	$2$	799.a	1.a	$1$	$1$	$1$	$6.380$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}+4q^{5}-2q^{6}-2q^{7}+\cdots\)
799.2.a.c	$799$	$2$	799.a	1.a	$1$	$2$	$2$	$6.380$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
799.2.a.d	$799$	$2$	799.a	1.a	$1$	$8$	$8$	$6.380$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(-7\)	\(-10\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{7})q^{4}+\cdots\)
799.2.a.e	$799$	$2$	799.a	1.a	$1$	$12$	$12$	$6.380$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(-1\)	\(-11\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
799.2.a.f	$799$	$2$	799.a	1.a	$1$	$17$	$17$	$6.380$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(1\)	\(11\)	\(1\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
799.2.a.g	$799$	$2$	799.a	1.a	$1$	$20$	$20$	$6.380$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(3\)	\(13\)	\(-3\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{17}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(799))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(799)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 2}\)