Space of modular forms of level 446, weight 2, and Character 446.c

• Label: 446.2.c
• Level: $446$
• Weight: $2$
• Character orbit: 446.c
• Rep. character: $\chi_{446}(39,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 223 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(446, [\chi])\).

	Total	New	Old
Modular forms	116	36	80
Cusp forms	108	36	72
Eisenstein series	8	0	8

Trace form

36 * q + 2 * q^3 + 36 * q^4 - 6 * q^5 - 6 * q^6 + 4 * q^7 - 26 * q^9 + 4 * q^11 + 2 * q^12 + 16 * q^13 - 12 * q^14 + 8 * q^15 + 36 * q^16 - 20 * q^17 + 8 * q^19 - 6 * q^20 - 16 * q^21 - 12 * q^22 - 2 * q^23 - 6 * q^24 - 36 * q^25 + 4 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^29 - 12 * q^30 - 34 * q^31 - 12 * q^33 + 2 * q^35 - 26 * q^36 - 20 * q^37 - 2 * q^38 + 6 * q^39 + 44 * q^41 - 14 * q^42 - 6 * q^43 + 4 * q^44 - 22 * q^45 + 12 * q^46 + 4 * q^47 + 2 * q^48 - 20 * q^49 - 8 * q^50 + 34 * q^51 + 16 * q^52 - 4 * q^53 + 48 * q^54 - 4 * q^55 - 12 * q^56 - 12 * q^57 + 6 * q^58 + 16 * q^59 + 8 * q^60 + 38 * q^61 + 12 * q^62 + 2 * q^63 + 36 * q^64 - 10 * q^65 + 16 * q^66 - 8 * q^67 - 20 * q^68 - 26 * q^69 + 16 * q^70 - 10 * q^71 + 6 * q^73 + 34 * q^75 + 8 * q^76 - 6 * q^77 + 12 * q^78 + 18 * q^79 - 6 * q^80 - 26 * q^81 + 8 * q^82 - 2 * q^83 - 16 * q^84 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 12 * q^88 + 4 * q^90 - 32 * q^91 - 2 * q^92 + 16 * q^93 - 22 * q^94 + 24 * q^95 - 6 * q^96 + 40 * q^97 + 16 * q^98 + 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(446, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
446.2.c.a	$446$	$2$	446.c	223.c	$3$	$2$	$1$	$3.561$	\(\Q(\sqrt{-3}) \)	None		✓			446.2.c.a	$2$	$0$	\(-2\)	\(1\)	\(1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
446.2.c.b	$446$	$2$	446.c	223.c	$3$	$2$	$1$	$3.561$	\(\Q(\sqrt{-3}) \)	None		✓			446.2.c.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+3\zeta_{6}q^{9}+2\zeta_{6}q^{11}+\cdots\)
446.2.c.c	$446$	$2$	446.c	223.c	$3$	$2$	$1$	$3.561$	\(\Q(\sqrt{-3}) \)	None		✓			446.2.c.c	$2$	$0$	\(2\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
446.2.c.d	$446$	$2$	446.c	223.c	$3$	$14$	$7$	$3.561$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			446.2.c.d	$2$	$0$	\(14\)	\(-3\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+\beta _{6}q^{3}+q^{4}+(-1-\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
446.2.c.e	$446$	$2$	446.c	223.c	$3$	$16$	$8$	$3.561$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		446.2.c.e	$2$	$0$	\(-16\)	\(3\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-\beta _{3}+\beta _{5})q^{3}+q^{4}+\beta _{13}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(446, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(446, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(223, [\chi])\)\(^{\oplus 2}\)