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

• Label: 841.2.d
• Level: $841$
• Weight: $2$
• Character orbit: 841.d
• Rep. character: $\chi_{841}(190,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $330$
• Newform subspaces: $17$
• Sturm bound: $145$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(145\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	522	486	36
Cusp forms	342	330	12
Eisenstein series	180	156	24

Trace form

330 * q + 2 * q^2 + 5 * q^3 - 40 * q^4 - q^5 + 3 * q^6 - q^7 + 7 * q^8 - 34 * q^9 - 9 * q^10 + 11 * q^11 - 4 * q^12 + 5 * q^13 - 9 * q^14 - 5 * q^15 - 18 * q^16 - 8 * q^17 + 9 * q^18 - q^19 - 2 * q^20 - 5 * q^21 - 12 * q^22 + 7 * q^23 - 13 * q^24 + 24 * q^25 - 4 * q^26 + 11 * q^27 + 48 * q^28 - 114 * q^30 - 5 * q^31 + 13 * q^32 - 7 * q^33 - 8 * q^34 + q^35 + 9 * q^36 - 11 * q^37 - 8 * q^38 - 3 * q^39 - 14 * q^40 - 20 * q^41 - 2 * q^42 - 13 * q^43 - 20 * q^44 - 7 * q^45 - 11 * q^47 - 6 * q^48 + 50 * q^49 - q^50 - 2 * q^51 + 4 * q^52 - 7 * q^53 - 12 * q^54 + 17 * q^55 + 7 * q^56 + 26 * q^57 - 100 * q^59 + 4 * q^60 - 3 * q^61 + 51 * q^62 - 19 * q^63 + 35 * q^64 - 11 * q^65 + 5 * q^66 - 21 * q^67 + 12 * q^68 + 7 * q^69 + 2 * q^70 - 25 * q^71 + 25 * q^73 + 4 * q^74 - 48 * q^75 + 5 * q^76 - 11 * q^77 - 25 * q^78 + 9 * q^79 + 8 * q^80 + 34 * q^81 - 8 * q^82 - 19 * q^83 - 3 * q^84 + 8 * q^85 + 76 * q^86 - 138 * q^88 - 7 * q^89 - 2 * q^90 - 17 * q^91 - 10 * q^92 + 7 * q^93 - 16 * q^94 - 13 * q^95 + 74 * q^96 - q^97 - 19 * q^98 + 32 * q^99

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.d.a	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$1$	\(-5\)	\(-2\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14})q^{2}+(-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{3}+\cdots\)
841.2.d.b	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$0$	\(-2\)	\(2\)	\(8\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\zeta_{14}^{3}-\zeta_{14}^{5})q^{2}+(-\zeta_{14}^{2}+\zeta_{14}^{3}+\cdots)q^{3}+\cdots\)
841.2.d.c	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$0$	\(2\)	\(-2\)	\(8\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots\)
841.2.d.d	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$0$	\(2\)	\(5\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
841.2.d.e	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$0$	\(5\)	\(2\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14})q^{2}+(\zeta_{14}-\zeta_{14}^{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
841.2.d.f	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.\(\cdots\).2	None					29.2.a.a	$6$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta _{1}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
841.2.d.g	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None		✓			841.2.a.a	$6$	$0$	\(-1\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots\)
841.2.d.h	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None					29.2.b.a	$12$	$0$	\(0\)	\(0\)	\(-6\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{6}q^{2}-\beta _{9}q^{3}+3\beta _{5}q^{4}+3\beta _{3}q^{5}+\cdots\)
841.2.d.i	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.\(\cdots\).1	None		✓			841.2.a.a	$6$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots\)
841.2.d.j	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.\(\cdots\).2	None					29.2.a.a	$6$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\beta _{2}+\beta _{9})q^{2}+(-\beta _{3}+\beta _{10})q^{3}+\cdots\)
841.2.d.k	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None					29.2.e.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(20\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.l	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None					29.2.e.a	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(-8\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.m	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None					29.2.e.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(-22\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.n	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		✓			841.2.a.g	$6$	$0$	\(-2\)	\(-2\)	\(2\)	\(4\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.o	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		✓			841.2.a.g	$6$	$0$	\(2\)	\(2\)	\(2\)	\(4\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.p	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		✓			841.2.a.i	$6$	$0$	\(-4\)	\(-6\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$
841.2.d.q	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		✓			841.2.a.i	$6$	$0$	\(4\)	\(6\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$

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

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