Space of modular forms of level 8015, weight 2, and trivial character

• Label: 8015.2.a
• Level: $8015$
• Weight: $2$
• Character orbit: 8015.a
• Rep. character: $\chi_{8015}(1,\cdot)$
• Character field: $\Q$
• Dimension: $455$
• Newform subspaces: $15$
• Sturm bound: $1840$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(1840\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8015))\).

	Total	New	Old
Modular forms	924	455	469
Cusp forms	917	455	462
Eisenstein series	7	0	7

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

\(5\)	\(7\)	\(229\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(52\)
\(+\)	\(+\)	\(-\)	$-$	\(63\)
\(+\)	\(-\)	\(+\)	$-$	\(68\)
\(+\)	\(-\)	\(-\)	$+$	\(45\)
\(-\)	\(+\)	\(+\)	$-$	\(67\)
\(-\)	\(+\)	\(-\)	$+$	\(44\)
\(-\)	\(-\)	\(+\)	$+$	\(41\)
\(-\)	\(-\)	\(-\)	$-$	\(75\)
Plus space			\(+\)	\(182\)
Minus space			\(-\)	\(273\)

Trace form

\( 455 q + 5 q^{2} + 4 q^{3} + 453 q^{4} - q^{5} + 20 q^{6} + 3 q^{7} + 33 q^{8} + 471 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7	229
8015.2.a.a	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-3\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
8015.2.a.b	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.c	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8015.2.a.d	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
8015.2.a.e	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
8015.2.a.f	$8015$	$2$	8015.a	1.a	$1$	$1$	$1$	$64.000$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.g	$8015$	$2$	8015.a	1.a	$1$	$3$	$3$	$64.000$	3.3.148.1	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
8015.2.a.h	$8015$	$2$	8015.a	1.a	$1$	$38$	$38$	$64.000$		None	✓	$1$	$1$	\(-6\)	\(-9\)	\(38\)	\(38\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8015.2.a.i	$8015$	$2$	8015.a	1.a	$1$	$44$	$44$	$64.000$		None	✓	$1$	$1$	\(-2\)	\(0\)	\(44\)	\(-44\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8015.2.a.j	$8015$	$2$	8015.a	1.a	$1$	$45$	$45$	$64.000$		None	✓	$1$	$1$	\(-6\)	\(0\)	\(-45\)	\(45\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8015.2.a.k	$8015$	$2$	8015.a	1.a	$1$	$49$	$49$	$64.000$		None	✓	$1$	$1$	\(-3\)	\(-10\)	\(-49\)	\(-49\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8015.2.a.l	$8015$	$2$	8015.a	1.a	$1$	$62$	$62$	$64.000$		None	✓	$1$	$0$	\(2\)	\(11\)	\(-62\)	\(-62\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8015.2.a.m	$8015$	$2$	8015.a	1.a	$1$	$67$	$67$	$64.000$		None	✓	$1$	$0$	\(3\)	\(0\)	\(67\)	\(-67\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8015.2.a.n	$8015$	$2$	8015.a	1.a	$1$	$68$	$68$	$64.000$		None	✓	$1$	$0$	\(9\)	\(0\)	\(-68\)	\(68\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8015.2.a.o	$8015$	$2$	8015.a	1.a	$1$	$73$	$73$	$64.000$		None	✓	$1$	$0$	\(7\)	\(14\)	\(73\)	\(73\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1603))\)\(^{\oplus 2}\)