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 - 124 * q^12 + 10 * q^13 - 22 * q^15 + 40 * q^16 + 10 * q^18 - 24 * q^20 - 64 * q^23 - 10 * q^25 - 28 * q^26 + 14 * q^27 - 50 * q^28 - 30 * q^30 + 28 * q^31 + 10 * q^35 - 24 * q^36 + 14 * q^37 - 10 * q^38 + 50 * q^40 - 40 * q^41 - 50 * q^42 - 28 * q^45 - 60 * q^46 + 20 * q^47 + 114 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 + 44 * q^53 - 48 * q^56 - 30 * q^57 + 26 * q^58 - 122 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 112 * q^67 + 30 * q^68 - 46 * q^70 - 28 * q^71 - 80 * q^72 - 50 * q^73 - 42 * q^75 - 236 * q^78 + 22 * q^80 - 68 * q^81 + 14 * q^82 - 90 * q^83 - 30 * q^85 - 108 * q^86 + 20 * q^90 - 4 * q^91 + 40 * q^92 + 26 * q^93 + 40 * q^95 + 14 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	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	\(\Q(\sqrt{-11}) \)					55.2.e.b	$16$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(\beta _{1}+\beta _{4}+\beta _{5})q^{3}+(-2\beta _{5}-2\beta _{7}+\cdots)q^{4}+\cdots\)
605.2.m.b	$605$	$2$	605.m	55.l	$20$	$16$	$2$	$4.831$	\(\Q(\zeta_{40})\)	None					55.2.e.a	$16$	$0$	\(0\)	\(4\)	\(8\)	\(0\)	$5^{4}$	$\mathrm{SU}(2)[C_{20}]$	\(q+(\beta_{15}+\beta_{12}+\cdots+\beta_{9})q^{2}+\cdots+(\beta_{6}+\beta_1)q^{3}+\cdots\)
605.2.m.c	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None					55.2.l.a	$4$	$0$	\(0\)	\(6\)	\(-2\)	\(-20\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.d	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None					55.2.l.a	$4$	$0$	\(0\)	\(6\)	\(-2\)	\(20\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.e	$605$	$2$	605.m	55.l	$20$	$32$	$4$	$4.831$		None					55.2.l.a	$4$	$0$	\(10\)	\(-4\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.f	$605$	$2$	605.m	55.l	$20$	$80$	$10$	$4.831$		None		✓			605.2.e.a	$16$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
605.2.m.g	$605$	$2$	605.m	55.l	$20$	$160$	$20$	$4.831$		None		✓	✓		605.2.e.c	$16$	$0$	\(0\)	\(-8\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

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

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