Space of modular forms of level 8092, weight 2, and trivial character

• Label: 8092.2.a
• Level: $8092$
• Weight: $2$
• Character orbit: 8092.a
• Rep. character: $\chi_{8092}(1,\cdot)$
• Character field: $\Q$
• Dimension: $136$
• Newform subspaces: $26$
• Sturm bound: $2448$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8092.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(2448\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8092))\).

	Total	New	Old
Modular forms	1278	136	1142
Cusp forms	1171	136	1035
Eisenstein series	107	0	107

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

\(2\)	\(7\)	\(17\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(-\)	\(32\)
\(-\)	\(+\)	\(-\)	\(+\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)	\(32\)
\(-\)	\(-\)	\(-\)	\(-\)	\(36\)
Plus space			\(+\)	\(68\)
Minus space			\(-\)	\(68\)

Trace form

136 * q + 4 * q^3 + 4 * q^5 + 140 * q^9 - 4 * q^11 - 12 * q^15 - 8 * q^23 + 152 * q^25 + 16 * q^27 + 4 * q^29 + 4 * q^31 - 8 * q^33 + 4 * q^35 + 8 * q^37 + 4 * q^39 - 4 * q^41 + 8 * q^43 - 16 * q^45 - 16 * q^47 + 136 * q^49 + 4 * q^53 + 8 * q^55 - 4 * q^57 + 16 * q^59 - 4 * q^61 - 8 * q^63 - 24 * q^65 + 12 * q^67 + 8 * q^71 - 4 * q^73 - 24 * q^75 + 4 * q^79 + 128 * q^81 - 20 * q^83 + 12 * q^87 + 40 * q^89 - 4 * q^91 - 8 * q^93 + 12 * q^95 + 28 * q^97 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8092))\) 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	7	17
8092.2.a.a	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots\)
8092.2.a.b	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{7}+q^{9}+4q^{13}+\cdots\)
8092.2.a.c	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.c	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8092.2.a.d	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.d	$1$	$2$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-6q^{11}-4q^{13}+\cdots\)
8092.2.a.e	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{19}+\cdots\)
8092.2.a.f	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.e	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{19}+\cdots\)
8092.2.a.g	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
8092.2.a.h	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots\)
8092.2.a.i	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}-q^{7}+q^{9}+4q^{13}+\cdots\)
8092.2.a.j	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	\(\Q\)	None	✓	✓			8092.2.a.a	$1$	$0$	\(0\)	\(3\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}+q^{7}+6q^{9}+4q^{13}+\cdots\)
8092.2.a.k	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(4+\cdots)q^{13}+\cdots\)
8092.2.a.l	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
8092.2.a.m	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	\(\Q(\sqrt{5}) \)	None	✓				476.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
8092.2.a.n	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.a	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-\beta )q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
8092.2.a.o	$8092$	$2$	8092.a	1.a	$1$	$3$	$3$	$64.615$	3.3.788.1	None	✓	✓			8092.2.a.o	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(3\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
8092.2.a.p	$8092$	$2$	8092.a	1.a	$1$	$3$	$3$	$64.615$	3.3.788.1	None	✓	✓			8092.2.a.o	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
8092.2.a.q	$8092$	$2$	8092.a	1.a	$1$	$4$	$4$	$64.615$	4.4.1957.1	None	✓				476.2.b.a	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+q^{7}+\cdots\)
8092.2.a.r	$8092$	$2$	8092.a	1.a	$1$	$4$	$4$	$64.615$	4.4.1957.1	None	✓				476.2.b.a	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(1-\beta _{3})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)
8092.2.a.s	$8092$	$2$	8092.a	1.a	$1$	$8$	$8$	$64.615$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				476.2.l.a	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(8\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-1-\beta _{1})q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
8092.2.a.t	$8092$	$2$	8092.a	1.a	$1$	$8$	$8$	$64.615$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				476.2.l.a	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-8\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
8092.2.a.u	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		8092.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}-q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.v	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8092.2.a.v	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-12\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{10}q^{5}-q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.w	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		8092.2.a.v	$1$	$1$	\(0\)	\(0\)	\(0\)	\(12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.x	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8092.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.y	$8092$	$2$	8092.a	1.a	$1$	$20$	$20$	$64.615$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		476.2.u.a	$1$	$1$	\(0\)	\(-8\)	\(-8\)	\(-20\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{12}q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
8092.2.a.z	$8092$	$2$	8092.a	1.a	$1$	$20$	$20$	$64.615$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		476.2.u.a	$1$	$0$	\(0\)	\(8\)	\(8\)	\(20\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{12}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8092))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8092)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\)\(^{\oplus 2}\)