Space of modular forms of level 2116, weight 4, and trivial character

• Label: 2116.4.a
• Level: $2116$
• Weight: $4$
• Character orbit: 2116.a
• Rep. character: $\chi_{2116}(1,\cdot)$
• Character field: $\Q$
• Dimension: $126$
• Newform subspaces: $10$
• Sturm bound: $1104$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2116 = 2^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2116.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1104\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2116))\).

	Total	New	Old
Modular forms	864	126	738
Cusp forms	792	126	666
Eisenstein series	72	0	72

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	Dim
\(-\)	\(+\)	\(-\)	\(60\)
\(-\)	\(-\)	\(+\)	\(66\)
Plus space		\(+\)	\(66\)
Minus space		\(-\)	\(60\)

Trace form

126 * q - 4 * q^3 + 10 * q^5 + 4 * q^7 + 1138 * q^9 + 58 * q^11 - 56 * q^13 + 128 * q^15 + 116 * q^17 - 26 * q^19 - 100 * q^21 + 3222 * q^25 - 424 * q^27 - 236 * q^29 + 172 * q^31 + 300 * q^33 + 60 * q^35 + 186 * q^37 - 288 * q^39 + 12 * q^41 + 498 * q^43 + 158 * q^45 + 596 * q^47 + 6006 * q^49 - 8 * q^51 - 234 * q^53 + 300 * q^55 + 16 * q^57 - 652 * q^59 + 714 * q^61 - 2052 * q^63 + 672 * q^65 + 1566 * q^67 - 1168 * q^71 + 332 * q^73 - 828 * q^75 + 728 * q^77 - 820 * q^79 + 9150 * q^81 + 950 * q^83 + 732 * q^85 - 480 * q^87 + 276 * q^89 - 696 * q^91 + 4044 * q^93 + 172 * q^95 - 2020 * q^97 + 4674 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2116))\) 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
2116.4.a.a	$2116$	$4$	2116.a	1.a	$1$	$3$	$3$	$124.848$	3.3.1229.1	None	✓				92.4.a.a	$1$	$0$	\(0\)	\(-4\)	\(10\)	\(46\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(4+\beta _{1}-3\beta _{2})q^{5}+\cdots\)
2116.4.a.b	$2116$	$4$	2116.a	1.a	$1$	$3$	$3$	$124.848$	3.3.28669.1	None	✓				92.4.a.b	$1$	$0$	\(0\)	\(8\)	\(0\)	\(-42\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta _{2})q^{3}-\beta _{1}q^{5}+(-14+\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.c	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2116.4.a.c	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-20\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{3})q^{5}+(-3+\cdots)q^{7}+\cdots\)
2116.4.a.d	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2116.4.a.c	$1$	$0$	\(0\)	\(1\)	\(5\)	\(20\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.e	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2116.4.a.e	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2116.4.a.f	$2116$	$4$	2116.a	1.a	$1$	$10$	$10$	$124.848$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			2116.4.a.f	$2$	$1$	\(0\)	\(-12\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.g	$2116$	$4$	2116.a	1.a	$1$	$12$	$12$	$124.848$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2116.4.a.g	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{14}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{3}+(\beta _{1}+\beta _{8})q^{5}+(-\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots\)
2116.4.a.h	$2116$	$4$	2116.a	1.a	$1$	$20$	$20$	$124.848$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			2116.4.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{23}\cdot 3^{2}\cdot 23^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+\beta _{11}q^{5}+(\beta _{12}+\beta _{15})q^{7}+\cdots\)
2116.4.a.i	$2116$	$4$	2116.a	1.a	$1$	$30$	$30$	$124.848$		None	✓		✓		92.4.e.a	$1$	$1$	\(0\)	\(-2\)	\(-50\)	\(2\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2116.4.a.j	$2116$	$4$	2116.a	1.a	$1$	$30$	$30$	$124.848$		None	✓		✓		92.4.e.a	$1$	$0$	\(0\)	\(-2\)	\(50\)	\(-2\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2116))\) into lower level spaces

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