Space of modular forms of level 8028, weight 2, and trivial character

• Label: 8028.2.a
• Level: $8028$
• Weight: $2$
• Character orbit: 8028.a
• Rep. character: $\chi_{8028}(1,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $16$
• Sturm bound: $2688$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8028.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2688\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8028))\).

	Total	New	Old
Modular forms	1356	92	1264
Cusp forms	1333	92	1241
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(223\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(-\)	$+$	\(18\)
\(-\)	\(-\)	\(+\)	$+$	\(28\)
\(-\)	\(-\)	\(-\)	$-$	\(28\)
Plus space			\(+\)	\(46\)
Minus space			\(-\)	\(46\)

Trace form

\( 92 q + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8028))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	223
8028.2.a.a	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-4q^{11}-6q^{17}-8q^{23}+\cdots\)
8028.2.a.b	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+3q^{11}+6q^{13}+7q^{17}+\cdots\)
8028.2.a.c	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-6q^{11}-6q^{13}-4q^{17}+\cdots\)
8028.2.a.d	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{11}-4q^{13}+3q^{17}+2q^{19}+\cdots\)
8028.2.a.e	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-q^{11}+3q^{17}-6q^{19}+q^{23}+\cdots\)
8028.2.a.f	$8028$	$2$	8028.a	1.a	$1$	$1$	$1$	$64.104$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}+4q^{11}+6q^{17}+8q^{23}+\cdots\)
8028.2.a.g	$8028$	$2$	8028.a	1.a	$1$	$2$	$2$	$64.104$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{7}-2\beta q^{11}+2q^{13}+2q^{19}+\cdots\)
8028.2.a.h	$8028$	$2$	8028.a	1.a	$1$	$2$	$2$	$64.104$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{5}+2\beta q^{7}+(4+\beta )q^{11}+\cdots\)
8028.2.a.i	$8028$	$2$	8028.a	1.a	$1$	$5$	$5$	$64.104$	5.5.1710888.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{4})q^{7}+(3+\cdots)q^{17}+\cdots\)
8028.2.a.j	$8028$	$2$	8028.a	1.a	$1$	$7$	$7$	$64.104$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(7\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}+\beta _{6})q^{5}+(\beta _{3}+\beta _{6})q^{7}+(1+\cdots)q^{11}+\cdots\)
8028.2.a.k	$8028$	$2$	8028.a	1.a	$1$	$8$	$8$	$64.104$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}+\beta _{3}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
8028.2.a.l	$8028$	$2$	8028.a	1.a	$1$	$8$	$8$	$64.104$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(5\)	\(-13\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{4}-\beta _{5})q^{5}+(-2+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
8028.2.a.m	$8028$	$2$	8028.a	1.a	$1$	$11$	$11$	$64.104$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}-\beta _{10}q^{7}+\beta _{7}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.n	$8028$	$2$	8028.a	1.a	$1$	$11$	$11$	$64.104$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(11\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(1+\beta _{9})q^{7}-\beta _{5}q^{11}+(1+\cdots)q^{13}+\cdots\)
8028.2.a.o	$8028$	$2$	8028.a	1.a	$1$	$16$	$16$	$64.104$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{15}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.p	$8028$	$2$	8028.a	1.a	$1$	$16$	$16$	$64.104$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(22\)		$-$	$+$	$+$	$-$	$7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(1-\beta _{7})q^{7}+\beta _{9}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(892))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\)\(^{\oplus 2}\)