Space of modular forms of level 1504, weight 2, and trivial character

• Label: 1504.2.a
• Level: $1504$
• Weight: $2$
• Character orbit: 1504.a
• Rep. character: $\chi_{1504}(1,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1504 = 2^{5} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1504.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1504))\).

	Total	New	Old
Modular forms	200	46	154
Cusp forms	185	46	139
Eisenstein series	15	0	15

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

\(2\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(10\)
\(+\)	\(-\)	$-$	\(14\)
\(-\)	\(+\)	$-$	\(13\)
\(-\)	\(-\)	$+$	\(9\)
Plus space		\(+\)	\(19\)
Minus space		\(-\)	\(27\)

Trace form

\( 46 q + 4 q^{5} + 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\) 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	47
1504.2.a.a	$1504$	$2$	1504.a	1.a	$1$	$4$	$4$	$12.010$	4.4.4752.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1504.2.a.b	$1504$	$2$	1504.a	1.a	$1$	$4$	$4$	$12.010$	4.4.4752.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1504.2.a.c	$1504$	$2$	1504.a	1.a	$1$	$5$	$5$	$12.010$	5.5.617072.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1504.2.a.d	$1504$	$2$	1504.a	1.a	$1$	$5$	$5$	$12.010$	5.5.617072.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots\)
1504.2.a.e	$1504$	$2$	1504.a	1.a	$1$	$6$	$6$	$12.010$	6.6.66862976.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{5}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1504.2.a.f	$1504$	$2$	1504.a	1.a	$1$	$6$	$6$	$12.010$	6.6.66862976.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{5}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1504.2.a.g	$1504$	$2$	1504.a	1.a	$1$	$8$	$8$	$12.010$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(8\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1+\beta _{7})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
1504.2.a.h	$1504$	$2$	1504.a	1.a	$1$	$8$	$8$	$12.010$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(6\)	\(-8\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1+\beta _{7})q^{5}+(-1-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1504))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1504)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 2}\)