Space of modular forms of level 1045, weight 4, and trivial character

• Label: 1045.4.a
• Level: $1045$
• Weight: $4$
• Character orbit: 1045.a
• Rep. character: $\chi_{1045}(1,\cdot)$
• Character field: $\Q$
• Dimension: $180$
• Newform subspaces: $9$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1045))\).

	Total	New	Old
Modular forms	364	180	184
Cusp forms	356	180	176
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.

\(5\)	\(11\)	\(19\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(25\)
\(-\)	\(+\)	\(+\)	\(-\)	\(22\)
\(-\)	\(+\)	\(-\)	\(+\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)	\(20\)
Plus space			\(+\)	\(94\)
Minus space			\(-\)	\(86\)

Trace form

\( 180 q + 720 q^{4} - 20 q^{5} - 136 q^{6} + 24 q^{8} + 1676 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1045))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	11	19
1045.4.a.a	$1045$	$4$	1045.a	1.a	$1$	$1$	$1$	$61.657$	\(\Q\)	None	✓	$1$	$1$	\(-5\)	\(-1\)	\(-5\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\)
1045.4.a.b	$1045$	$4$	1045.a	1.a	$1$	$20$	$20$	$61.657$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-12\)	\(-21\)	\(100\)	\(-131\)		$-$	$-$	$-$	$-$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots\)
1045.4.a.c	$1045$	$4$	1045.a	1.a	$1$	$20$	$20$	$61.657$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-8\)	\(-100\)	\(49\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1045.4.a.d	$1045$	$4$	1045.a	1.a	$1$	$22$	$22$	$61.657$		None	✓	$1$	$1$	\(-4\)	\(-21\)	\(110\)	\(-41\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
1045.4.a.e	$1045$	$4$	1045.a	1.a	$1$	$22$	$22$	$61.657$		None	✓	$1$	$0$	\(12\)	\(21\)	\(110\)	\(93\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
1045.4.a.f	$1045$	$4$	1045.a	1.a	$1$	$23$	$23$	$61.657$		None	✓	$1$	$1$	\(-2\)	\(-9\)	\(-115\)	\(13\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
1045.4.a.g	$1045$	$4$	1045.a	1.a	$1$	$23$	$23$	$61.657$		None	✓	$1$	$0$	\(6\)	\(9\)	\(-115\)	\(-37\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
1045.4.a.h	$1045$	$4$	1045.a	1.a	$1$	$24$	$24$	$61.657$		None	✓	$1$	$0$	\(4\)	\(21\)	\(120\)	\(71\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
1045.4.a.i	$1045$	$4$	1045.a	1.a	$1$	$25$	$25$	$61.657$		None	✓	$1$	$0$	\(2\)	\(9\)	\(-125\)	\(-15\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1045))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1045)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)