Space of modular forms of level 1700, weight 2, and Character 1700.e

• Label: 1700.2.e
• Level: $1700$
• Weight: $2$
• Character orbit: 1700.e
• Rep. character: $\chi_{1700}(749,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $540$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1700.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(540\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1700, [\chi])\).

	Total	New	Old
Modular forms	288	24	264
Cusp forms	252	24	228
Eisenstein series	36	0	36

Trace form

24 * q - 36 * q^9 + 4 * q^11 - 16 * q^19 + 20 * q^21 - 4 * q^29 + 8 * q^31 - 8 * q^39 + 12 * q^41 - 52 * q^49 - 4 * q^51 - 8 * q^59 + 8 * q^61 - 64 * q^69 - 4 * q^71 + 40 * q^79 + 136 * q^81 - 56 * q^89 + 48 * q^91 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1700, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1700.2.e.a	$1700$	$2$	1700.e	5.b	$2$	$2$	$2$	$13.575$	\(\Q(\sqrt{-1}) \)	None		✓			1700.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{7}+2 q^{9}-i q^{13}+i q^{17}+\cdots\)
1700.2.e.b	$1700$	$2$	1700.e	5.b	$2$	$2$	$2$	$13.575$	\(\Q(\sqrt{-1}) \)	None					340.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4 i q^{7}+3 q^{9}+2 q^{11}+6 i q^{13}+\cdots\)
1700.2.e.c	$1700$	$2$	1700.e	5.b	$2$	$4$	$4$	$13.575$	\(\Q(\zeta_{12})\)	None					68.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}+(-\beta_{2}+\beta_1)q^{7}+\cdots\)
1700.2.e.d	$1700$	$2$	1700.e	5.b	$2$	$6$	$6$	$13.575$	6.0.2611456.1	None					340.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{2}q^{7}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
1700.2.e.e	$1700$	$2$	1700.e	5.b	$2$	$10$	$10$	$13.575$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		1700.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{8}q^{7}+(-3+\beta _{4}-\beta _{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 2}\)