Space of modular forms of level 1665, weight 2, and Character 1665.c

• Label: 1665.2.c
• Level: $1665$
• Weight: $2$
• Character orbit: 1665.c
• Rep. character: $\chi_{1665}(334,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $7$
• Sturm bound: $456$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(456\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1665, [\chi])\).

	Total	New	Old
Modular forms	236	90	146
Cusp forms	220	90	130
Eisenstein series	16	0	16

Trace form

90 * q - 86 * q^4 + 2 * q^5 - 18 * q^10 - 8 * q^11 + 102 * q^16 + 8 * q^19 - 4 * q^20 + 14 * q^25 - 12 * q^26 + 12 * q^29 - 12 * q^31 - 28 * q^34 + 6 * q^35 + 50 * q^40 - 4 * q^41 + 24 * q^44 + 16 * q^46 - 122 * q^49 + 36 * q^50 - 18 * q^55 - 24 * q^56 - 20 * q^59 - 16 * q^61 - 110 * q^64 + 4 * q^65 + 32 * q^70 + 8 * q^71 - 10 * q^74 - 32 * q^76 + 20 * q^79 + 52 * q^80 + 32 * q^85 - 80 * q^86 - 16 * q^89 + 76 * q^91 + 52 * q^94 + 20 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1665, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1665.2.c.a	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None					555.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+(2 i+1)q^{5}+(2 i-4)q^{10}+\cdots\)
1665.2.c.b	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None		✓			1665.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}+(2 i-1)q^{5}+2 i q^{7}-6 q^{11}+\cdots\)
1665.2.c.c	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	\(\Q(\sqrt{-1}) \)	None		✓			1665.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}+(2 i+1)q^{5}-2 i q^{7}+6 q^{11}+\cdots\)
1665.2.c.d	$1665$	$2$	1665.c	5.b	$2$	$8$	$8$	$13.295$	8.0.309760000.3	None					555.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1665.2.c.e	$1665$	$2$	1665.c	5.b	$2$	$18$	$18$	$13.295$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					185.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{13})q^{2}+(-2+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1665.2.c.f	$1665$	$2$	1665.c	5.b	$2$	$26$	$26$	$13.295$		None					555.2.c.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1665.2.c.g	$1665$	$2$	1665.c	5.b	$2$	$32$	$32$	$13.295$		None		✓	✓		1665.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1665, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1665, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)