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

• Label: 841.2.e
• Level: $841$
• Weight: $2$
• Character orbit: 841.e
• Rep. character: $\chi_{841}(63,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $324$
• Newform subspaces: $13$
• Sturm bound: $145$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(145\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	528	480	48
Cusp forms	348	324	24
Eisenstein series	180	156	24

Trace form

\( 324 q + 7 q^{2} + 7 q^{3} + 43 q^{4} + q^{5} + 3 q^{6} + 11 q^{7} - 14 q^{8} + 31 q^{9} + O(q^{10}) \)

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	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.e.a	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(-7\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1+2\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{9}+\cdots)q^{2}+\cdots\)
841.2.e.b	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	\(\Q(\zeta_{28})\)	None					29.2.d.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\zeta_{28}^{7}+\zeta_{28}^{9})q^{2}+(-\zeta_{28}-\zeta_{28}^{9}+\cdots)q^{3}+\cdots\)
841.2.e.c	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	\(\Q(\zeta_{28})\)	None					29.2.d.a	$4$	$0$	\(0\)	\(0\)	\(-16\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\zeta_{28}-\zeta_{28}^{5}+\zeta_{28}^{7}-\zeta_{28}^{9}+\cdots)q^{2}+\cdots\)
841.2.e.d	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	\(\Q(\zeta_{28})\)	None					29.2.d.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{2}+(\zeta_{28}^{7}+\zeta_{28}^{11})q^{3}+\cdots\)
841.2.e.e	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(\beta _{4}-\beta _{10}+\beta _{11})q^{2}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
841.2.e.f	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\beta _{4}-\beta _{8}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
841.2.e.g	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).3	None					29.2.b.a	$12$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+3\beta _{2}q^{4}-3\beta _{8}q^{5}+\cdots\)
841.2.e.h	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(7\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1-2\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
841.2.e.i	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(7\)	\(7\)	\(-1\)	\(-11\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1-\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{2}+(-1+\cdots)q^{3}+\cdots\)
841.2.e.j	$841$	$2$	841.e	29.e	$14$	$24$	$4$	$6.715$		None		✓			841.2.a.a	$12$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
841.2.e.k	$841$	$2$	841.e	29.e	$14$	$24$	$4$	$6.715$		None					29.2.a.a	$12$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
841.2.e.l	$841$	$2$	841.e	29.e	$14$	$72$	$12$	$6.715$		None		✓			841.2.a.g	$12$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)		$\mathrm{SU}(2)[C_{14}]$
841.2.e.m	$841$	$2$	841.e	29.e	$14$	$96$	$16$	$6.715$		None		✓	✓		841.2.a.i	$12$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

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

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