Space of modular forms of level 2107, weight 4, and trivial character

• Label: 2107.4.a
• Level: $2107$
• Weight: $4$
• Character orbit: 2107.a
• Rep. character: $\chi_{2107}(1,\cdot)$
• Character field: $\Q$
• Dimension: $430$
• Newform subspaces: $15$
• Sturm bound: $821$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 2107 = 7^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2107.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(821\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2107))\).

	Total	New	Old
Modular forms	624	430	194
Cusp forms	608	430	178
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.

\(7\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(108\)
\(+\)	\(-\)	$-$	\(100\)
\(-\)	\(+\)	$-$	\(108\)
\(-\)	\(-\)	$+$	\(114\)
Plus space		\(+\)	\(222\)
Minus space		\(-\)	\(208\)

Trace form

\( 430 q + 2 q^{2} - 4 q^{3} + 1704 q^{4} + 16 q^{5} - 6 q^{6} + 72 q^{8} + 3916 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2107))\) 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	43
2107.4.a.a	$2107$	$4$	2107.a	1.a	$1$	$1$	$1$	$124.317$	\(\Q\)	None	✓	$1$	$0$	\(3\)	\(-10\)	\(-6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-10q^{3}+q^{4}-6q^{5}-30q^{6}+\cdots\)
2107.4.a.b	$2107$	$4$	2107.a	1.a	$1$	$4$	$4$	$124.317$	4.4.45868.1	None	✓	$1$	$0$	\(-4\)	\(11\)	\(27\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+\cdots\)
2107.4.a.c	$2107$	$4$	2107.a	1.a	$1$	$6$	$6$	$124.317$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(6\)	\(-7\)	\(-43\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
2107.4.a.d	$2107$	$4$	2107.a	1.a	$1$	$14$	$14$	$124.317$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-10\)	\(11\)	\(23\)	\(0\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
2107.4.a.e	$2107$	$4$	2107.a	1.a	$1$	$16$	$16$	$124.317$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(-4\)	\(9\)	\(43\)	\(0\)		$-$	$-$	$+$	$2\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
2107.4.a.f	$2107$	$4$	2107.a	1.a	$1$	$16$	$16$	$124.317$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-15\)	\(-7\)	\(0\)		$-$	$+$	$-$	$2^{2}\cdot 3^{3}\cdot 13$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2107.4.a.g	$2107$	$4$	2107.a	1.a	$1$	$17$	$17$	$124.317$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(9\)	\(-3\)	\(-21\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{7}q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2107.4.a.h	$2107$	$4$	2107.a	1.a	$1$	$30$	$30$	$124.317$		None	✓	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2107.4.a.i	$2107$	$4$	2107.a	1.a	$1$	$34$	$34$	$124.317$		None	✓	$2$	$0$	\(12\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2107.4.a.j	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		None	✓	$1$	$1$	\(0\)	\(-18\)	\(-70\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2107.4.a.k	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		None	✓	$1$	$1$	\(0\)	\(-18\)	\(-70\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2107.4.a.l	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		None	✓	$1$	$0$	\(0\)	\(18\)	\(70\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2107.4.a.m	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		None	✓	$1$	$0$	\(0\)	\(18\)	\(70\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2107.4.a.n	$2107$	$4$	2107.a	1.a	$1$	$58$	$58$	$124.317$		None	✓	$2$	$1$	\(-20\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2107.4.a.o	$2107$	$4$	2107.a	1.a	$1$	$66$	$66$	$124.317$		None	✓	$2$	$0$	\(20\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2107))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2107)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(301))\)\(^{\oplus 2}\)