Space of modular forms of level 841, weight 2, and trivial character

• Label: 841.2.a
• Level: $841$
• Weight: $2$
• Character orbit: 841.a
• Rep. character: $\chi_{841}(1,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $11$
• Sturm bound: $145$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(145\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(841))\).

	Total	New	Old
Modular forms	87	81	6
Cusp forms	58	54	4
Eisenstein series	29	27	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(29\)	Dim
\(+\)	\(24\)
\(-\)	\(30\)

Trace form

\( 54 q + 2 q^{2} - 2 q^{3} + 40 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} + 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(841))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		29
841.2.a.a	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots\)
841.2.a.b	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)		$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+\beta q^{3}+3q^{4}+3q^{5}-5q^{6}+\cdots\)
841.2.a.c	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots\)
841.2.a.d	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
841.2.a.e	$841$	$2$	841.a	1.a	$1$	$3$	$3$	$6.715$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(-3\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
841.2.a.f	$841$	$2$	841.a	1.a	$1$	$3$	$3$	$6.715$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-3\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
841.2.a.g	$841$	$2$	841.a	1.a	$1$	$6$	$6$	$6.715$	6.6.11973625.1	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
841.2.a.h	$841$	$2$	841.a	1.a	$1$	$6$	$6$	$6.715$	6.6.11973625.1	None	✓	$1$	$0$	\(2\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
841.2.a.i	$841$	$2$	841.a	1.a	$1$	$8$	$8$	$6.715$	8.8.2841328125.1	None	✓	$1$	$1$	\(-4\)	\(-6\)	\(-1\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
841.2.a.j	$841$	$2$	841.a	1.a	$1$	$8$	$8$	$6.715$	8.8.2841328125.1	None	✓	$1$	$0$	\(4\)	\(6\)	\(-1\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
841.2.a.k	$841$	$2$	841.a	1.a	$1$	$12$	$12$	$6.715$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(8\)	\(10\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{11}q^{2}+(-\beta _{6}-\beta _{9})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(841))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(841)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)