Space of modular forms of level 2151, weight 2, and trivial character

• Label: 2151.2.a
• Level: $2151$
• Weight: $2$
• Character orbit: 2151.a
• Rep. character: $\chi_{2151}(1,\cdot)$
• Character field: $\Q$
• Dimension: $99$
• Newform subspaces: $11$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2151 = 3^{2} \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2151.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2151))\).

	Total	New	Old
Modular forms	244	99	145
Cusp forms	237	99	138
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.

\(3\)	\(239\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(20\)
\(+\)	\(-\)	$-$	\(20\)
\(-\)	\(+\)	$-$	\(37\)
\(-\)	\(-\)	$+$	\(22\)
Plus space		\(+\)	\(42\)
Minus space		\(-\)	\(57\)

Trace form

\( 99 q + 94 q^{4} - 6 q^{7} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2151))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	239
2151.2.a.a	$2151$	$2$	2151.a	1.a	$1$	$2$	$2$	$17.176$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
2151.2.a.b	$2151$	$2$	2151.a	1.a	$1$	$2$	$2$	$17.176$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-6\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-3q^{5}+(2-2\beta )q^{7}+\cdots\)
2151.2.a.c	$2151$	$2$	2151.a	1.a	$1$	$2$	$2$	$17.176$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
2151.2.a.d	$2151$	$2$	2151.a	1.a	$1$	$3$	$3$	$17.176$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
2151.2.a.e	$2151$	$2$	2151.a	1.a	$1$	$6$	$6$	$17.176$	6.6.1767625.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(-5\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2151.2.a.f	$2151$	$2$	2151.a	1.a	$1$	$7$	$7$	$17.176$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1+\beta _{6})q^{4}-\beta _{6}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2151.2.a.g	$2151$	$2$	2151.a	1.a	$1$	$8$	$8$	$17.176$	8.8.2585660609.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(13\)	\(-7\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
2151.2.a.h	$2151$	$2$	2151.a	1.a	$1$	$12$	$12$	$17.176$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(1\)	\(11\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)
2151.2.a.i	$2151$	$2$	2151.a	1.a	$1$	$17$	$17$	$17.176$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+(1+\cdots)q^{7}+\cdots\)
2151.2.a.j	$2151$	$2$	2151.a	1.a	$1$	$20$	$20$	$17.176$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-16\)	\(-4\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{9})q^{5}+\cdots\)
2151.2.a.k	$2151$	$2$	2151.a	1.a	$1$	$20$	$20$	$17.176$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(16\)	\(-4\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2151))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2151)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(717))\)\(^{\oplus 2}\)