Space of modular forms of level 4015, weight 2, and trivial character

• Label: 4015.2.a
• Level: $4015$
• Weight: $2$
• Character orbit: 4015.a
• Rep. character: $\chi_{4015}(1,\cdot)$
• Character field: $\Q$
• Dimension: $239$
• Newform subspaces: $9$
• Sturm bound: $888$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(888\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4015))\).

	Total	New	Old
Modular forms	448	239	209
Cusp forms	441	239	202
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.

\(5\)	\(11\)	\(73\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(32\)
\(+\)	\(+\)	\(-\)	$-$	\(27\)
\(+\)	\(-\)	\(+\)	$-$	\(27\)
\(+\)	\(-\)	\(-\)	$+$	\(32\)
\(-\)	\(+\)	\(+\)	$-$	\(38\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(23\)
\(-\)	\(-\)	\(-\)	$-$	\(37\)
Plus space			\(+\)	\(110\)
Minus space			\(-\)	\(129\)

Trace form

\( 239 q - 3 q^{2} - 4 q^{3} + 241 q^{4} + 3 q^{5} + 4 q^{6} - 8 q^{7} - 15 q^{8} + 235 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\) 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	11	73
4015.2.a.a	$4015$	$2$	4015.a	1.a	$1$	$1$	$1$	$32.060$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-3q^{7}-2q^{9}+q^{11}+\cdots\)
4015.2.a.b	$4015$	$2$	4015.a	1.a	$1$	$23$	$23$	$32.060$		None	✓	$1$	$1$	\(-5\)	\(-3\)	\(23\)	\(-10\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
4015.2.a.c	$4015$	$2$	4015.a	1.a	$1$	$23$	$23$	$32.060$		None	✓	$1$	$1$	\(-3\)	\(-5\)	\(23\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
4015.2.a.d	$4015$	$2$	4015.a	1.a	$1$	$27$	$27$	$32.060$		None	✓	$1$	$0$	\(2\)	\(3\)	\(-27\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4015.2.a.e	$4015$	$2$	4015.a	1.a	$1$	$27$	$27$	$32.060$		None	✓	$1$	$0$	\(6\)	\(5\)	\(-27\)	\(10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4015.2.a.f	$4015$	$2$	4015.a	1.a	$1$	$31$	$31$	$32.060$		None	✓	$1$	$1$	\(-7\)	\(-4\)	\(-31\)	\(-11\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4015.2.a.g	$4015$	$2$	4015.a	1.a	$1$	$32$	$32$	$32.060$		None	✓	$1$	$1$	\(-5\)	\(-7\)	\(-32\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4015.2.a.h	$4015$	$2$	4015.a	1.a	$1$	$37$	$37$	$32.060$		None	✓	$1$	$0$	\(5\)	\(3\)	\(37\)	\(6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
4015.2.a.i	$4015$	$2$	4015.a	1.a	$1$	$38$	$38$	$32.060$		None	✓	$1$	$0$	\(4\)	\(5\)	\(38\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(803))\)\(^{\oplus 2}\)