Space of modular forms of level 418, weight 2, and Character 418.f

• Label: 418.2.f
• Level: $418$
• Weight: $2$
• Character orbit: 418.f
• Rep. character: $\chi_{418}(115,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $72$
• Newform subspaces: $8$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(418, [\chi])\).

	Total	New	Old
Modular forms	256	72	184
Cusp forms	224	72	152
Eisenstein series	32	0	32

Trace form

72 * q + 4 * q^3 - 18 * q^4 + 8 * q^5 + 4 * q^6 + 2 * q^7 - 38 * q^9 + 8 * q^10 - 6 * q^11 - 16 * q^12 - 12 * q^13 - 28 * q^15 - 18 * q^16 + 10 * q^17 + 16 * q^18 + 2 * q^19 + 8 * q^20 + 56 * q^21 + 4 * q^22 + 20 * q^23 + 4 * q^24 + 6 * q^25 - 24 * q^26 - 20 * q^27 - 8 * q^28 + 16 * q^29 + 8 * q^30 - 48 * q^33 + 16 * q^34 - 30 * q^35 + 2 * q^36 + 12 * q^37 + 48 * q^39 - 12 * q^40 - 4 * q^41 - 36 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 24 * q^46 - 32 * q^47 + 4 * q^48 - 16 * q^51 + 8 * q^52 + 36 * q^53 - 64 * q^54 + 18 * q^55 + 4 * q^57 - 40 * q^58 + 20 * q^59 + 32 * q^60 - 38 * q^61 + 40 * q^62 - 42 * q^63 - 18 * q^64 - 56 * q^65 - 4 * q^66 - 136 * q^67 + 10 * q^68 + 72 * q^69 + 12 * q^71 - 24 * q^72 - 16 * q^73 - 4 * q^74 + 124 * q^75 - 8 * q^76 + 68 * q^77 + 8 * q^78 + 96 * q^79 - 2 * q^80 + 30 * q^81 + 28 * q^83 - 24 * q^84 + 30 * q^85 - 4 * q^86 + 120 * q^87 + 4 * q^88 - 28 * q^90 - 36 * q^91 - 20 * q^92 - 48 * q^93 + 32 * q^94 - 6 * q^95 + 4 * q^96 - 76 * q^97 + 64 * q^98 + 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(418, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
418.2.f.a	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	\(\Q(\zeta_{10})\)	None		✓			418.2.f.a	$2$	$1$	\(-1\)	\(-4\)	\(-8\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.b	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	\(\Q(\zeta_{10})\)	None		✓			418.2.f.b	$2$	$0$	\(-1\)	\(0\)	\(8\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.c	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	\(\Q(\zeta_{10})\)	None		✓			418.2.f.c	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.d	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	\(\Q(\zeta_{10})\)	None		✓			418.2.f.d	$2$	$0$	\(-1\)	\(2\)	\(2\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.e	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	\(\Q(\zeta_{10})\)	None		✓			418.2.f.e	$2$	$0$	\(-1\)	\(5\)	\(3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.f	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			418.2.f.f	$2$	$0$	\(-4\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
418.2.f.g	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			418.2.f.g	$2$	$0$	\(4\)	\(1\)	\(1\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{6}-\beta _{8}+\beta _{10})q^{2}+\beta _{1}q^{3}+\cdots\)
418.2.f.h	$418$	$2$	418.f	11.c	$5$	$20$	$5$	$3.338$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		418.2.f.h	$2$	$0$	\(5\)	\(-1\)	\(-1\)	\(13\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{9}q^{2}-\beta _{4}q^{3}+(-1+\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(418, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(418, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)