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

\( 68 q - 68 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 74 q^{9} + O(q^{10}) \)

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

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

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