Space of modular forms of level 605, weight 2, and Character 605.j

• Label: 605.2.j
• Level: $605$
• Weight: $2$
• Character orbit: 605.j
• Rep. character: $\chi_{605}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $184$
• Newform subspaces: $11$
• Sturm bound: $132$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(132\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

	Total	New	Old
Modular forms	312	248	64
Cusp forms	216	184	32
Eisenstein series	96	64	32

Trace form

\( 184 q + 44 q^{4} + 3 q^{5} + 18 q^{6} + 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
605.2.j.a	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.484000000.6	\(\Q(\sqrt{-55}) \)		$8$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.b	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.228765625.1	\(\Q(\sqrt{-11}) \)		$16$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.j.c	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.484000000.6	\(\Q(\sqrt{-55}) \)		$8$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.d	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots\)
605.2.j.e	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.f	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.g	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{13}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.j.h	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{13}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.j.i	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots\)
605.2.j.j	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots\)
605.2.j.k	$605$	$2$	605.j	55.j	$10$	$48$	$12$	$4.831$		None		$16$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)