Space of modular forms of level 1682, weight 2, and Character 1682.b

• Label: 1682.2.b
• Level: $1682$
• Weight: $2$
• Character orbit: 1682.b
• Rep. character: $\chi_{1682}(1681,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $11$
• Sturm bound: $435$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1682.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(435\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1682, [\chi])\).

	Total	New	Old
Modular forms	248	68	180
Cusp forms	188	68	120
Eisenstein series	60	0	60

Trace form

68 * q - 68 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 74 * q^9 + 2 * q^13 + 68 * q^16 + 2 * q^20 - 10 * q^22 + 12 * q^23 - 2 * q^24 + 78 * q^25 - 4 * q^28 - 4 * q^30 - 4 * q^33 - 4 * q^34 + 4 * q^35 + 74 * q^36 + 14 * q^38 - 4 * q^42 - 10 * q^45 + 76 * q^49 + 4 * q^51 - 2 * q^52 - 6 * q^53 + 4 * q^54 + 16 * q^57 - 22 * q^59 + 12 * q^62 + 16 * q^63 - 68 * q^64 - 4 * q^65 - 14 * q^67 + 24 * q^71 + 14 * q^74 - 8 * q^78 - 2 * q^80 + 60 * q^81 - 20 * q^82 - 30 * q^83 - 18 * q^86 + 10 * q^88 - 4 * q^91 - 12 * q^92 + 24 * q^93 + 4 * q^94 + 2 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(1682, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1682.2.b.a	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	\(\Q(\sqrt{-1}) \)	None					58.2.a.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}-q^{5}+q^{6}+\cdots\)
1682.2.b.b	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	\(\Q(\sqrt{-1}) \)	None		✓			1682.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-q^{7}+\cdots\)
1682.2.b.c	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	\(\Q(\sqrt{-1}) \)	None		✓			1682.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+3 i q^{3}-q^{4}+3 q^{6}+4 q^{7}+\cdots\)
1682.2.b.d	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	\(\Q(\sqrt{-1}) \)	None		✓			1682.2.a.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}+2 q^{5}-2 q^{6}+\cdots\)
1682.2.b.e	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	\(\Q(\sqrt{-1}) \)	None					58.2.a.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}+3 q^{5}-3 q^{6}+\cdots\)
1682.2.b.f	$1682$	$2$	1682.b	29.b	$2$	$4$	$4$	$13.431$	\(\Q(i, \sqrt{5})\)	None		✓			1682.2.a.k	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-2q^{5}+\beta _{2}q^{6}+\cdots\)
1682.2.b.g	$1682$	$2$	1682.b	29.b	$2$	$6$	$6$	$13.431$	6.0.153664.1	None					58.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(\beta _{3}+\beta _{5})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
1682.2.b.h	$1682$	$2$	1682.b	29.b	$2$	$8$	$8$	$13.431$	8.0.324000000.1	None		✓			1682.2.a.o	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
1682.2.b.i	$1682$	$2$	1682.b	29.b	$2$	$12$	$12$	$13.431$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					58.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{4}+\beta _{11})q^{5}+\cdots\)
1682.2.b.j	$1682$	$2$	1682.b	29.b	$2$	$12$	$12$	$13.431$	\(\Q(\zeta_{28})\)	None					58.2.e.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+(-\beta_{3}-\beta_1)q^{3}-q^{4}+\cdots\)
1682.2.b.k	$1682$	$2$	1682.b	29.b	$2$	$16$	$16$	$13.431$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		1682.2.a.u	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{13}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1682, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1682, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(841, [\chi])\)\(^{\oplus 2}\)