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 + 2 * q^13 + 16 * q^16 - 18 * q^20 + 4 * q^22 - 12 * q^23 + 16 * q^24 - 8 * q^25 + 6 * q^28 + 8 * q^30 - 16 * q^33 - 26 * q^34 + 12 * q^35 - 26 * q^36 - 6 * q^38 - 26 * q^42 - 6 * q^45 - 22 * q^49 + 16 * q^51 + 22 * q^53 - 4 * q^54 - 4 * q^57 - 38 * q^59 + 84 * q^62 + 4 * q^63 + 10 * q^64 - 18 * q^67 - 4 * q^71 + 2 * q^74 + 22 * q^78 - 16 * q^80 - 30 * q^81 - 10 * q^82 + 14 * q^83 - 40 * q^86 - 26 * q^88 - 8 * q^91 + 26 * q^92 - 40 * q^93 + 18 * q^94 + 102 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	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					29.2.a.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-\beta_1 q^{3}+(-\beta_{3}-1)q^{4}+\cdots\)
841.2.b.b	$841$	$2$	841.b	29.b	$2$	$4$	$4$	$6.715$	\(\Q(i, \sqrt{5})\)	None		✓			841.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
841.2.b.c	$841$	$2$	841.b	29.b	$2$	$6$	$6$	$6.715$	6.0.153664.1	None					29.2.d.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
841.2.b.d	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			841.2.a.g	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
841.2.b.e	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(10\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{11})q^{2}+(-\beta _{5}+\beta _{11})q^{3}+\cdots\)
841.2.b.f	$841$	$2$	841.b	29.b	$2$	$16$	$16$	$6.715$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		841.2.a.i	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{9}-\beta _{15})q^{3}+(-1+\cdots)q^{4}+\cdots\)

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

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