Space of modular forms of level 2493, weight 2, and trivial character

• Label: 2493.2.a
• Level: $2493$
• Weight: $2$
• Character orbit: 2493.a
• Rep. character: $\chi_{2493}(1,\cdot)$
• Character field: $\Q$
• Dimension: $115$
• Newform subspaces: $11$
• Sturm bound: $556$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2493 = 3^{2} \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2493.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(556\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2493))\).

	Total	New	Old
Modular forms	282	115	167
Cusp forms	275	115	160
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.

\(3\)	\(277\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(20\)
\(+\)	\(-\)	$-$	\(26\)
\(-\)	\(+\)	$-$	\(36\)
\(-\)	\(-\)	$+$	\(33\)
Plus space		\(+\)	\(53\)
Minus space		\(-\)	\(62\)

Trace form

\( 115 q - q^{2} + 111 q^{4} - 4 q^{5} - 4 q^{7} + 3 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2493))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	277
2493.2.a.a	$2493$	$2$	2493.a	1.a	$1$	$1$	$1$	$19.907$	\(\Q\)	None	✓		277.2.a.a	$1$	$2$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}-4q^{7}+3q^{8}+2q^{10}+\cdots\)
2493.2.a.b	$2493$	$2$	2493.a	1.a	$1$	$1$	$1$	$19.907$	\(\Q\)	None	✓		831.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{7}-3q^{8}+3q^{11}+\cdots\)
2493.2.a.c	$2493$	$2$	2493.a	1.a	$1$	$3$	$3$	$19.907$	\(\Q(\zeta_{18})^+\)	None	✓		831.2.a.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2493.2.a.d	$2493$	$2$	2493.a	1.a	$1$	$3$	$3$	$19.907$	3.3.148.1	None	✓		277.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
2493.2.a.e	$2493$	$2$	2493.a	1.a	$1$	$6$	$6$	$19.907$	6.6.5740564.1	None	✓		831.2.a.c	$1$	$0$	\(1\)	\(0\)	\(3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2493.2.a.f	$2493$	$2$	2493.a	1.a	$1$	$9$	$9$	$19.907$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		277.2.a.d	$1$	$1$	\(-4\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{5}+\beta _{6})q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots\)
2493.2.a.g	$2493$	$2$	2493.a	1.a	$1$	$9$	$9$	$19.907$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		277.2.a.c	$1$	$0$	\(6\)	\(0\)	\(12\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2493.2.a.h	$2493$	$2$	2493.a	1.a	$1$	$17$	$17$	$19.907$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		831.2.a.d	$1$	$1$	\(-4\)	\(0\)	\(-9\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
2493.2.a.i	$2493$	$2$	2493.a	1.a	$1$	$20$	$20$	$19.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		831.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(11\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+(1+\cdots)q^{7}+\cdots\)
2493.2.a.j	$2493$	$2$	2493.a	1.a	$1$	$20$	$20$	$19.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	2493.2.a.j	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-18\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2493.2.a.k	$2493$	$2$	2493.a	1.a	$1$	$26$	$26$	$19.907$		None	✓	✓	2493.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2493))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2493)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(277))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(831))\)\(^{\oplus 2}\)