Space of modular forms of level 2116, weight 2, and trivial character

• Label: 2116.2.a
• Level: $2116$
• Weight: $2$
• Character orbit: 2116.a
• Rep. character: $\chi_{2116}(1,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $10$
• Sturm bound: $552$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2116 = 2^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2116.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(552\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2116))\).

	Total	New	Old
Modular forms	312	42	270
Cusp forms	241	42	199
Eisenstein series	71	0	71

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

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(78\)	\(0\)	\(78\)		\(55\)	\(0\)	\(55\)		\(23\)	\(0\)	\(23\)
\(+\)	\(-\)	\(-\)		\(84\)	\(0\)	\(84\)		\(60\)	\(0\)	\(60\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)		\(78\)	\(24\)	\(54\)		\(66\)	\(24\)	\(42\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)		\(72\)	\(18\)	\(54\)		\(60\)	\(18\)	\(42\)		\(12\)	\(0\)	\(12\)
Plus space		\(+\)		\(150\)	\(18\)	\(132\)		\(115\)	\(18\)	\(97\)		\(35\)	\(0\)	\(35\)
Minus space		\(-\)		\(162\)	\(24\)	\(138\)		\(126\)	\(24\)	\(102\)		\(36\)	\(0\)	\(36\)

Trace form

42 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 + 40 * q^9 - 2 * q^11 + 6 * q^13 - 6 * q^15 + 2 * q^17 - 14 * q^21 + 50 * q^25 + 14 * q^27 + 12 * q^29 + 6 * q^33 - 6 * q^35 - 10 * q^37 - 14 * q^39 + 8 * q^41 + 12 * q^45 - 22 * q^47 + 40 * q^49 + 18 * q^51 - 8 * q^53 - 8 * q^57 + 14 * q^59 - 12 * q^61 + 28 * q^63 - 10 * q^65 - 22 * q^67 + 16 * q^71 + 2 * q^73 + 10 * q^75 + 16 * q^77 + 16 * q^79 + 42 * q^81 - 14 * q^83 + 2 * q^85 - 10 * q^87 - 12 * q^89 - 18 * q^91 - 14 * q^93 + 10 * q^97 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2116))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	23
2116.2.a.a	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	None	✓				92.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+4q^{7}+6q^{9}-2q^{11}+\cdots\)
2116.2.a.b	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	None	✓	✓			2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
2116.2.a.c	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	None	✓	✓			2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
2116.2.a.d	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots\)
2116.2.a.e	$2116$	$2$	2116.a	1.a	$1$	$2$	$2$	$16.896$	\(\Q(\sqrt{3}) \)	None	✓	✓			2116.2.a.e	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+q^{13}+\cdots\)
2116.2.a.f	$2116$	$2$	2116.a	1.a	$1$	$2$	$2$	$16.896$	\(\Q(\sqrt{3}) \)	None	✓	✓			2116.2.a.f	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+\beta q^{7}-2q^{9}+\beta q^{11}+\cdots\)
2116.2.a.g	$2116$	$2$	2116.a	1.a	$1$	$6$	$6$	$16.896$	6.6.197448192.1	None	✓	✓			2116.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
2116.2.a.h	$2116$	$2$	2116.a	1.a	$1$	$8$	$8$	$16.896$	8.8.5780865024.1	None	✓	✓			2116.2.a.h	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{5})q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
2116.2.a.i	$2116$	$2$	2116.a	1.a	$1$	$10$	$10$	$16.896$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		92.2.e.a	$1$	$1$	\(0\)	\(1\)	\(-12\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
2116.2.a.j	$2116$	$2$	2116.a	1.a	$1$	$10$	$10$	$16.896$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		92.2.e.a	$1$	$0$	\(0\)	\(1\)	\(12\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2116)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)