Space of modular forms of level 4284, weight 2, and Character 4284.d

• Label: 4284.2.d
• Level: $4284$
• Weight: $2$
• Character orbit: 4284.d
• Rep. character: $\chi_{4284}(3025,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $7$
• Sturm bound: $1728$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4284.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1728\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4284, [\chi])\).

	Total	New	Old
Modular forms	888	44	844
Cusp forms	840	44	796
Eisenstein series	48	0	48

Trace form

\( 44 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4284, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4284.2.d.a	$4284$	$2$	4284.d	17.b	$2$	$2$	$2$	$34.208$	\(\Q(\sqrt{-1}) \)	None					1428.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+4iq^{11}-2q^{13}+(-1-4i)q^{17}+\cdots\)
4284.2.d.b	$4284$	$2$	4284.d	17.b	$2$	$2$	$2$	$34.208$	\(\Q(\sqrt{-1}) \)	None		✓			4284.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}-iq^{7}-3iq^{11}-q^{13}+(-4+\cdots)q^{17}+\cdots\)
4284.2.d.c	$4284$	$2$	4284.d	17.b	$2$	$2$	$2$	$34.208$	\(\Q(\sqrt{-1}) \)	None		✓			4284.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}+iq^{7}-3iq^{11}-q^{13}+(4+\cdots)q^{17}+\cdots\)
4284.2.d.d	$4284$	$2$	4284.d	17.b	$2$	$6$	$6$	$34.208$	6.0.38738176.1	None					1428.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{1}q^{7}+(-3\beta _{1}-\beta _{4}+\beta _{5})q^{11}+\cdots\)
4284.2.d.e	$4284$	$2$	4284.d	17.b	$2$	$8$	$8$	$34.208$	8.0.980441344.2	None					476.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{4}q^{7}+(-2\beta _{4}+\beta _{6}+\beta _{7})q^{11}+\cdots\)
4284.2.d.f	$4284$	$2$	4284.d	17.b	$2$	$12$	$12$	$34.208$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					1428.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{8}q^{7}+(\beta _{2}-\beta _{8})q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)
4284.2.d.g	$4284$	$2$	4284.d	17.b	$2$	$12$	$12$	$34.208$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			4284.2.d.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}-\beta _{3}q^{7}+(-\beta _{5}+\beta _{8})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4284, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4284, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1071, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1428, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2142, [\chi])\)\(^{\oplus 2}\)