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

• Label: 605.2.g
• Level: $605$
• Weight: $2$
• Character orbit: 605.g
• Rep. character: $\chi_{605}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $144$
• Newform subspaces: $17$
• Sturm bound: $132$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(132\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	312	144	168
Cusp forms	216	144	72
Eisenstein series	96	0	96

Trace form

144 * q + 6 * q^2 + 4 * q^3 - 32 * q^4 - 6 * q^6 + 4 * q^7 - 2 * q^8 - 30 * q^9 - 8 * q^10 + 12 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 20 * q^16 + 12 * q^17 - 14 * q^18 - 14 * q^19 + 8 * q^20 + 32 * q^21 - 8 * q^23 - 38 * q^24 - 36 * q^25 + 12 * q^26 - 20 * q^27 + 2 * q^28 - 10 * q^29 + 20 * q^30 + 8 * q^31 - 28 * q^32 - 32 * q^34 + 12 * q^35 - 26 * q^36 - 20 * q^37 + 30 * q^38 - 30 * q^39 + 6 * q^40 - 4 * q^41 - 10 * q^42 - 4 * q^43 + 38 * q^46 + 4 * q^47 + 34 * q^48 - 14 * q^49 + 6 * q^50 - 14 * q^51 + 54 * q^52 - 12 * q^53 + 24 * q^54 - 180 * q^56 + 50 * q^57 + 6 * q^58 + 58 * q^59 - 26 * q^60 - 4 * q^61 + 68 * q^62 - 26 * q^63 - 12 * q^64 - 16 * q^65 + 24 * q^67 - 46 * q^68 + 30 * q^69 - 28 * q^70 - 8 * q^71 + 64 * q^72 + 10 * q^73 - 68 * q^74 - 6 * q^75 - 16 * q^76 - 140 * q^78 - 54 * q^79 - 8 * q^80 - 32 * q^81 - 22 * q^82 - 2 * q^83 - 24 * q^84 + 16 * q^85 + 58 * q^86 - 68 * q^87 - 48 * q^89 + 26 * q^90 - 96 * q^91 - 60 * q^92 - 8 * q^93 - 50 * q^94 + 16 * q^95 - 6 * q^96 - 88 * q^97 + 68 * q^98

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.g.a	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	\(\Q(\zeta_{10})\)	None					55.2.a.a	$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.b	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	\(\Q(\zeta_{10})\)	None		✓			605.2.a.a	$4$	$0$	\(-1\)	\(3\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.c	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	\(\Q(\zeta_{10})\)	None					55.2.a.a	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
605.2.g.d	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	\(\Q(\zeta_{10})\)	None		✓			605.2.a.a	$4$	$0$	\(1\)	\(3\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots\)
605.2.g.e	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	None					55.2.g.b	$2$	$0$	\(-3\)	\(5\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.f	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.64000000.2	None					55.2.a.b	$4$	$0$	\(-2\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.g	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	None					55.2.g.a	$2$	$0$	\(-1\)	\(1\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.h	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.324000000.3	None		✓			605.2.a.f	$8$	$0$	\(0\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.i	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.324000000.3	None		✓			605.2.a.e	$8$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.j	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	None					55.2.g.a	$2$	$0$	\(1\)	\(1\)	\(-2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.k	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	None					55.2.g.b	$2$	$0$	\(2\)	\(-5\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
605.2.g.l	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.64000000.2	None					55.2.a.b	$4$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.g.m	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	None					55.2.g.b	$2$	$0$	\(3\)	\(5\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.n	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	None					55.2.g.a	$2$	$0$	\(4\)	\(1\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
605.2.g.o	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			605.2.a.g	$4$	$0$	\(-1\)	\(-1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.g.p	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			605.2.a.g	$4$	$0$	\(1\)	\(-1\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.g.q	$605$	$2$	605.g	11.c	$5$	$24$	$6$	$4.831$		None		✓	✓		605.2.a.m	$8$	$0$	\(0\)	\(-6\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(605, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)