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

• Label: 1710.2.t
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.t
• Rep. character: $\chi_{1710}(919,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $5$
• Sturm bound: $720$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(720\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	752	100	652
Cusp forms	688	100	588
Eisenstein series	64	0	64

Trace form

100 * q + 50 * q^4 - 2 * q^5 - 12 * q^11 + 6 * q^14 - 50 * q^16 + 26 * q^19 - 4 * q^20 - 6 * q^25 + 8 * q^26 + 20 * q^29 + 16 * q^31 - 8 * q^34 - 14 * q^35 + 2 * q^41 - 6 * q^44 + 12 * q^46 - 104 * q^49 - 40 * q^50 - 30 * q^55 + 12 * q^56 + 20 * q^59 + 12 * q^61 - 100 * q^64 - 40 * q^65 - 20 * q^71 - 22 * q^74 + 4 * q^76 + 12 * q^79 - 2 * q^80 + 36 * q^85 + 8 * q^86 + 50 * q^89 + 28 * q^91 + 56 * q^94 + 56 * 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.t.a	$1710$	$2$	1710.t	95.i	$6$	$8$	$4$	$13.654$	\(\Q(\zeta_{24})\)	None					570.2.q.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{2}+\beta_{2} q^{4}+(\beta_{6}+\beta_{2}+\beta_1-1)q^{5}+\cdots\)
1710.2.t.b	$1710$	$2$	1710.t	95.i	$6$	$12$	$6$	$13.654$	12.0.\(\cdots\).1	None					570.2.q.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+\beta _{8}q^{4}+(\beta _{6}-\beta _{11})q^{5}+(3\beta _{4}+\cdots)q^{7}+\cdots\)
1710.2.t.c	$1710$	$2$	1710.t	95.i	$6$	$20$	$10$	$13.654$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					570.2.q.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+\beta _{12}q^{4}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
1710.2.t.d	$1710$	$2$	1710.t	95.i	$6$	$20$	$10$	$13.654$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					190.2.i.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{13})q^{2}+(1-\beta _{3})q^{4}+\beta _{14}q^{5}+\cdots\)
1710.2.t.e	$1710$	$2$	1710.t	95.i	$6$	$40$	$20$	$13.654$		None		✓	✓		1710.2.t.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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