Space of modular forms of level 105, weight 4, and trivial character

• Label: 105.4.a
• Level: $105$
• Weight: $4$
• Character orbit: 105.a
• Rep. character: $\chi_{105}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $7$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(105))\).

	Total	New	Old
Modular forms	52	12	40
Cusp forms	44	12	32
Eisenstein series	8	0	8

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

\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
Plus space			\(+\)	\(8\)
Minus space			\(-\)	\(4\)

Trace form

\( 12 q - 4 q^{2} + 56 q^{4} + 12 q^{6} - 28 q^{7} + 36 q^{8} + 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\) 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	5	7
105.4.a.a	$105$	$4$	105.a	1.a	$1$	$1$	$1$	$6.195$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-8q^{4}+5q^{5}+7q^{7}+9q^{9}+\cdots\)
105.4.a.b	$105$	$4$	105.a	1.a	$1$	$1$	$1$	$6.195$	\(\Q\)	None	✓	$1$	$0$	\(5\)	\(-3\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
105.4.a.c	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-7\)	\(-6\)	\(-10\)	\(-14\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}-3q^{3}+(5+7\beta )q^{4}+\cdots\)
105.4.a.d	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-4\)	\(6\)	\(-10\)	\(-14\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
105.4.a.e	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-6\)	\(10\)	\(-14\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
105.4.a.f	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{65}) \)	None	✓	$1$	$0$	\(1\)	\(6\)	\(10\)	\(-14\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3q^{3}+(8+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
105.4.a.g	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(3\)	\(6\)	\(-10\)	\(14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}-5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(105))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(105)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)