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

• Label: 605.2.m
• Level: $605$
• Weight: $2$
• Character orbit: 605.m
• Rep. character: $\chi_{605}(112,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $368$
• Newform subspaces: $7$
• Sturm bound: $132$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(132\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	624	496	128
Cusp forms	432	368	64
Eisenstein series	192	128	64

Trace form

\( 368 q + 10 q^{2} + 2 q^{3} + 2 q^{5} + 20 q^{6} + 10 q^{8} + O(q^{10}) \)

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.m.a	$605$	$2$	605.m	55.l	$20$	$16$	$2$	$4.831$	16.0.\(\cdots\).1	\(\Q(\sqrt{-11}) \)		$16$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(\beta _{1}+\beta _{4}+\beta _{5})q^{3}+(-2\beta _{5}-2\beta _{7}+\cdots)q^{4}+\cdots\)
605.2.m.b	$605$	$2$	605.m	55.l	$20$	$16$	$2$	$4.831$	\(\Q(\zeta_{40})\)	None		$16$	$0$	\(0\)	\(4\)	\(8\)	\(0\)	$5^{4}$	$\mathrm{SU}(2)[C_{20}]$	\(q+(\zeta_{40}^{9}+\zeta_{40}^{11}+\zeta_{40}^{12}+\zeta_{40}^{15})q^{2}+\cdots\)
605.2.m.c	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None		$4$	$0$	\(0\)	\(6\)	\(-2\)	\(-20\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.d	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None		$4$	$0$	\(0\)	\(6\)	\(-2\)	\(20\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.e	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None		$4$	$0$	\(10\)	\(-4\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.f	$605$	$2$	605.m	55.l	$20$	$80$	$10$	$4.831$		None		$16$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.g	$605$	$2$	605.m	55.l	$20$	$160$	$20$	$4.831$		None		$16$	$0$	\(0\)	\(-8\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

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

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