Space of modular forms of level 803, weight 2, and trivial character

• Label: 803.2.a
• Level: $803$
• Weight: $2$
• Character orbit: 803.a
• Rep. character: $\chi_{803}(1,\cdot)$
• Character field: $\Q$
• Dimension: $61$
• Newform subspaces: $6$
• Sturm bound: $148$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 803 = 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	803.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(148\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(803))\).

	Total	New	Old
Modular forms	76	61	15
Cusp forms	73	61	12
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.

\(11\)	\(73\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(11\)
\(+\)	\(-\)	$-$	\(21\)
\(-\)	\(+\)	$-$	\(19\)
\(-\)	\(-\)	$+$	\(10\)
Plus space		\(+\)	\(21\)
Minus space		\(-\)	\(40\)

Trace form

\( 61 q + 3 q^{2} + 2 q^{3} + 59 q^{4} - 4 q^{6} + 8 q^{7} + 3 q^{8} + 63 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(803))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	73
803.2.a.a	$803$	$2$	803.a	1.a	$1$	$2$	$2$	$6.412$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(-2\)	\(1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}-q^{4}-2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
803.2.a.b	$803$	$2$	803.a	1.a	$1$	$5$	$5$	$6.412$	5.5.3714917.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-2q^{4}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
803.2.a.c	$803$	$2$	803.a	1.a	$1$	$9$	$9$	$6.412$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(-5\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
803.2.a.d	$803$	$2$	803.a	1.a	$1$	$10$	$10$	$6.412$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(-3\)	\(-2\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
803.2.a.e	$803$	$2$	803.a	1.a	$1$	$16$	$16$	$6.412$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
803.2.a.f	$803$	$2$	803.a	1.a	$1$	$19$	$19$	$6.412$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(3\)	\(2\)	\(16\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{15}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(803)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 2}\)