Space of modular forms of level 4284, weight 2, and trivial character

• Label: 4284.2.a
• Level: $4284$
• Weight: $2$
• Character orbit: 4284.a
• Rep. character: $\chi_{4284}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $22$
• Sturm bound: $1728$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4284.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1728\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4284))\).

	Total	New	Old
Modular forms	888	40	848
Cusp forms	841	40	801
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(7\)	\(17\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(6\)
Plus space				\(+\)	\(20\)
Minus space				\(-\)	\(20\)

Trace form

40 * q + 4 * q^5 - 4 * q^11 + 4 * q^13 + 4 * q^19 + 28 * q^25 - 4 * q^29 - 4 * q^31 - 4 * q^35 - 8 * q^37 + 4 * q^41 - 4 * q^43 + 24 * q^47 + 40 * q^49 - 20 * q^53 - 12 * q^55 - 8 * q^59 - 28 * q^61 - 72 * q^65 - 4 * q^67 + 32 * q^71 - 12 * q^73 - 20 * q^79 - 28 * q^83 + 8 * q^85 + 48 * q^89 + 4 * q^91 + 4 * q^95 - 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4284))\) 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					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	17
4284.2.a.a	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓	✓			4284.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-2q^{11}-6q^{13}-q^{17}+\cdots\)
4284.2.a.b	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓				1428.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+6q^{13}+q^{17}-2q^{19}+\cdots\)
4284.2.a.c	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓				1428.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-2q^{13}+q^{17}+6q^{19}+\cdots\)
4284.2.a.d	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓	✓			4284.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+2q^{11}+2q^{13}-q^{17}+\cdots\)
4284.2.a.e	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓				1428.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+q^{11}-7q^{13}+q^{17}+\cdots\)
4284.2.a.f	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓	✓			4284.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+2q^{11}-6q^{13}+q^{17}+\cdots\)
4284.2.a.g	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓	✓			4284.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-2q^{11}+2q^{13}+q^{17}+\cdots\)
4284.2.a.h	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓				1428.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}+5q^{11}+q^{13}+q^{17}+\cdots\)
4284.2.a.i	$4284$	$2$	4284.a	1.a	$1$	$1$	$1$	$34.208$	\(\Q\)	None	✓				1428.2.a.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
4284.2.a.j	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{17}) \)	None	✓				1428.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+(-1+\beta )q^{11}+\cdots\)
4284.2.a.k	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{10}) \)	None	✓				1428.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}-3q^{11}+(3-\beta )q^{13}+\cdots\)
4284.2.a.l	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}-4q^{11}+(-2+2\beta )q^{13}+\cdots\)
4284.2.a.m	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{5}) \)	None	✓				476.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(2+2\beta )q^{11}-2\beta q^{13}+\cdots\)
4284.2.a.n	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}+(2+2\beta )q^{13}-q^{17}+\cdots\)
4284.2.a.o	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{2}) \)	None	✓				1428.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(1-2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
4284.2.a.p	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}-2\beta q^{11}+(-2-2\beta )q^{13}+\cdots\)
4284.2.a.q	$4284$	$2$	4284.a	1.a	$1$	$2$	$2$	$34.208$	\(\Q(\sqrt{3}) \)	None	✓				1428.2.a.f	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}-q^{7}+(-3-2\beta )q^{11}+\cdots\)
4284.2.a.r	$4284$	$2$	4284.a	1.a	$1$	$3$	$3$	$34.208$	3.3.3028.1	None	✓	✓	✓		4284.2.a.r	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}+q^{7}-3q^{11}-\beta _{2}q^{13}+\cdots\)
4284.2.a.s	$4284$	$2$	4284.a	1.a	$1$	$3$	$3$	$34.208$	3.3.4764.1	None	✓		✓		1428.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+q^{7}+(1+\beta _{2})q^{11}+\cdots\)
4284.2.a.t	$4284$	$2$	4284.a	1.a	$1$	$3$	$3$	$34.208$	3.3.404.1	None	✓	✓	✓		4284.2.a.t	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}-q^{7}+(-3+2\beta _{1})q^{11}+(2+\cdots)q^{13}+\cdots\)
4284.2.a.u	$4284$	$2$	4284.a	1.a	$1$	$3$	$3$	$34.208$	3.3.404.1	None	✓	✓	✓		4284.2.a.t	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-q^{7}+(3-2\beta _{1})q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots\)
4284.2.a.v	$4284$	$2$	4284.a	1.a	$1$	$3$	$3$	$34.208$	3.3.3028.1	None	✓	✓	✓		4284.2.a.r	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+q^{7}+3q^{11}-\beta _{2}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4284))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4284)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1071))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1428))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2142))\)\(^{\oplus 2}\)