Space of modular forms of level 1710, weight 2, and Character 1710.d

• Label: 1710.2.d
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.d
• Rep. character: $\chi_{1710}(1369,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

	Total	New	Old
Modular forms	376	46	330
Cusp forms	344	46	298
Eisenstein series	32	0	32

Trace form

46 * q - 46 * q^4 - 6 * q^5 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 46 * q^16 - 2 * q^19 + 6 * q^20 - 18 * q^25 - 20 * q^26 + 4 * q^29 + 16 * q^31 - 20 * q^35 - 4 * q^40 + 12 * q^41 - 8 * q^44 - 4 * q^46 - 46 * q^49 + 8 * q^50 - 8 * q^55 + 4 * q^56 + 24 * q^59 + 4 * q^61 - 46 * q^64 - 44 * q^65 + 16 * q^70 + 32 * q^71 + 12 * q^74 + 2 * q^76 + 24 * q^79 - 6 * q^80 + 4 * q^85 + 20 * q^86 + 20 * q^89 - 64 * q^91 + 12 * q^94 - 2 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1710.2.d.a	$1710$	$2$	1710.d	5.b	$2$	$2$	$2$	$13.654$	\(\Q(\sqrt{-1}) \)	None					570.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(i-2)q^{5}-i q^{8}+\cdots\)
1710.2.d.b	$1710$	$2$	1710.d	5.b	$2$	$2$	$2$	$13.654$	\(\Q(\sqrt{-1}) \)	None					570.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{8}+\cdots\)
1710.2.d.c	$1710$	$2$	1710.d	5.b	$2$	$4$	$4$	$13.654$	\(\Q(\zeta_{8})\)	None					190.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1710.2.d.d	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.5161984.1	None					190.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1710.2.d.e	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.350464.1	None					570.2.d.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.f	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.350464.1	None					570.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.g	$1710$	$2$	1710.d	5.b	$2$	$8$	$8$	$13.654$	\(\Q(\zeta_{24})\)	None		✓			1710.2.d.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-q^{4}+\beta_{7} q^{5}+(-\beta_{6}+\beta_{3}+\beta_{2})q^{7}+\cdots\)
1710.2.d.h	$1710$	$2$	1710.d	5.b	$2$	$12$	$12$	$13.654$	12.0.\(\cdots\).1	None		✓	✓		1710.2.d.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)