Space of modular forms of level 2303, weight 4, and trivial character

• Label: 2303.4.a
• Level: $2303$
• Weight: $4$
• Character orbit: 2303.a
• Rep. character: $\chi_{2303}(1,\cdot)$
• Character field: $\Q$
• Dimension: $471$
• Newform subspaces: $14$
• Sturm bound: $896$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(896\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2303))\).

	Total	New	Old
Modular forms	680	471	209
Cusp forms	664	471	193
Eisenstein series	16	0	16

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

\(7\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(119\)
\(+\)	\(-\)	$-$	\(109\)
\(-\)	\(+\)	$-$	\(114\)
\(-\)	\(-\)	$+$	\(129\)
Plus space		\(+\)	\(248\)
Minus space		\(-\)	\(223\)

Trace form

\( 471 q + 2 q^{2} + 2 q^{3} + 1870 q^{4} + 8 q^{5} + 32 q^{6} - 18 q^{8} + 4191 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2303))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	47
2303.4.a.a	$2303$	$4$	2303.a	1.a	$1$	$3$	$3$	$135.881$	3.3.1101.1	None	✓	$1$	$1$	\(-5\)	\(5\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
2303.4.a.b	$2303$	$4$	2303.a	1.a	$1$	$8$	$8$	$135.881$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-7\)	\(-14\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
2303.4.a.c	$2303$	$4$	2303.a	1.a	$1$	$14$	$14$	$135.881$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(10\)	\(4\)	\(0\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
2303.4.a.d	$2303$	$4$	2303.a	1.a	$1$	$15$	$15$	$135.881$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(16\)	\(24\)	\(0\)		$-$	$-$	$+$	$2^{6}\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
2303.4.a.e	$2303$	$4$	2303.a	1.a	$1$	$20$	$20$	$135.881$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-2\)	\(4\)	\(0\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots\)
2303.4.a.f	$2303$	$4$	2303.a	1.a	$1$	$21$	$21$	$135.881$		None	✓	$1$	$1$	\(2\)	\(-20\)	\(-16\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2303.4.a.g	$2303$	$4$	2303.a	1.a	$1$	$35$	$35$	$135.881$		None	✓	$1$	$1$	\(5\)	\(-12\)	\(-20\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2303.4.a.h	$2303$	$4$	2303.a	1.a	$1$	$35$	$35$	$135.881$		None	✓	$1$	$0$	\(5\)	\(12\)	\(20\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2303.4.a.i	$2303$	$4$	2303.a	1.a	$1$	$41$	$41$	$135.881$		None	✓	$1$	$1$	\(-9\)	\(-6\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2303.4.a.j	$2303$	$4$	2303.a	1.a	$1$	$41$	$41$	$135.881$		None	✓	$1$	$1$	\(-9\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2303.4.a.k	$2303$	$4$	2303.a	1.a	$1$	$51$	$51$	$135.881$		None	✓	$1$	$0$	\(7\)	\(-6\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2303.4.a.l	$2303$	$4$	2303.a	1.a	$1$	$51$	$51$	$135.881$		None	✓	$1$	$0$	\(7\)	\(6\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2303.4.a.m	$2303$	$4$	2303.a	1.a	$1$	$68$	$68$	$135.881$		None	✓	$1$	$1$	\(-2\)	\(-24\)	\(-40\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2303.4.a.n	$2303$	$4$	2303.a	1.a	$1$	$68$	$68$	$135.881$		None	✓	$1$	$0$	\(-2\)	\(24\)	\(40\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2303))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2303)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(329))\)\(^{\oplus 2}\)