Space of modular forms of level 441, weight 2, and Character 441.bb

• Label: 441.2.bb
• Level: $441$
• Weight: $2$
• Character orbit: 441.bb
• Rep. character: $\chi_{441}(37,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $264$
• Newform subspaces: $6$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

	Total	New	Old
Modular forms	720	288	432
Cusp forms	624	264	360
Eisenstein series	96	24	72

Trace form

264 * q + 13 * q^2 + 7 * q^4 + 16 * q^5 - 8 * q^7 + 8 * q^8 - 18 * q^10 + 23 * q^11 - 2 * q^13 - 19 * q^14 + 9 * q^16 + 21 * q^17 + 15 * q^19 + 34 * q^20 - 16 * q^22 - 7 * q^23 - 2 * q^25 + 26 * q^26 - 72 * q^28 - 28 * q^29 + 37 * q^31 + 61 * q^32 - 42 * q^34 + 26 * q^35 - 61 * q^37 - 30 * q^38 + 14 * q^40 - 34 * q^41 - 34 * q^43 - 34 * q^44 - 98 * q^46 - 29 * q^47 + 44 * q^49 + 148 * q^50 + 114 * q^52 - 51 * q^53 + 13 * q^55 - 140 * q^56 + 72 * q^58 + 12 * q^59 + 45 * q^61 + 8 * q^62 + 32 * q^64 + 16 * q^65 + q^67 - 77 * q^68 - 82 * q^70 + 41 * q^71 - 3 * q^73 + 28 * q^74 + 3 * q^76 + 27 * q^77 - 7 * q^79 - 120 * q^80 - 174 * q^82 - 58 * q^83 - 74 * q^85 - 51 * q^86 - 137 * q^88 - 72 * q^89 - 142 * q^91 - 46 * q^92 - 222 * q^94 - 125 * q^95 - 16 * q^97 - 185 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.2.bb.a	$441$	$2$	441.bb	49.g	$21$	$12$	$1$	$3.521$	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-3}) \)		✓			441.2.bb.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{21}]$	\(q+(2-2\zeta_{21}^{2}+2\zeta_{21}^{3}-2\zeta_{21}^{5}+2\zeta_{21}^{6}+\cdots)q^{4}+\cdots\)
441.2.bb.b	$441$	$2$	441.bb	49.g	$21$	$24$	$2$	$3.521$		None		✓			441.2.bb.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(28\)		$\mathrm{SU}(2)[C_{21}]$
441.2.bb.c	$441$	$2$	441.bb	49.g	$21$	$48$	$4$	$3.521$		None					147.2.m.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
441.2.bb.d	$441$	$2$	441.bb	49.g	$21$	$48$	$4$	$3.521$		None					49.2.g.a	$2$	$0$	\(13\)	\(0\)	\(14\)	\(-14\)		$\mathrm{SU}(2)[C_{21}]$
441.2.bb.e	$441$	$2$	441.bb	49.g	$21$	$60$	$5$	$3.521$		None					147.2.m.b	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(5\)		$\mathrm{SU}(2)[C_{21}]$
441.2.bb.f	$441$	$2$	441.bb	49.g	$21$	$72$	$6$	$3.521$		None		✓	✓		441.2.bb.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(441, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)