Space of modular forms of level 841, weight 2, and Character 841.b

• Label: 841.2.b
• Level: $841$
• Weight: $2$
• Character orbit: 841.b
• Rep. character: $\chi_{841}(840,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $6$
• Sturm bound: $145$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(145\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(841, [\chi])\).

	Total	New	Old
Modular forms	88	80	8
Cusp forms	58	54	4
Eisenstein series	30	26	4

Trace form

\( 54 q - 36 q^{4} + 6 q^{5} - 10 q^{6} - 4 q^{7} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(841, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
841.2.b.a	$841$	$2$	841.b	29.b	$2$	$4$	$4$	$6.715$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
841.2.b.b	$841$	$2$	841.b	29.b	$2$	$4$	$4$	$6.715$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
841.2.b.c	$841$	$2$	841.b	29.b	$2$	$6$	$6$	$6.715$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
841.2.b.d	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
841.2.b.e	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(10\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{11})q^{2}+(-\beta _{5}+\beta _{11})q^{3}+\cdots\)
841.2.b.f	$841$	$2$	841.b	29.b	$2$	$16$	$16$	$6.715$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{9}-\beta _{15})q^{3}+(-1+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(841, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(841, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)