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

• Label: 441.2.bn
• Level: $441$
• Weight: $2$
• Character orbit: 441.bn
• Rep. character: $\chi_{441}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $648$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bn (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	696	696	0
Cusp forms	648	648	0
Eisenstein series	48	48	0

Trace form

648 * q - 21 * q^2 - 11 * q^3 + 99 * q^4 - 18 * q^5 - 34 * q^6 - 5 * q^7 - 23 * q^9 - 22 * q^10 - 18 * q^11 - 72 * q^12 - 4 * q^13 + 66 * q^14 - 10 * q^15 - 105 * q^16 - 9 * q^17 - 27 * q^18 - 36 * q^19 - 27 * q^20 - 11 * q^21 - 9 * q^22 - 27 * q^23 - 8 * q^24 + 38 * q^25 + 6 * q^26 - 29 * q^27 - 26 * q^28 + 3 * q^29 - 16 * q^30 - 21 * q^32 - 11 * q^33 - 13 * q^34 + 28 * q^36 - 13 * q^37 - 90 * q^38 - 15 * q^39 - 31 * q^40 - 27 * q^41 - 4 * q^42 - 9 * q^43 + 51 * q^44 - 11 * q^45 - 108 * q^46 + 75 * q^47 - 15 * q^48 - 13 * q^49 - 45 * q^50 - 38 * q^51 + 64 * q^52 - 12 * q^53 - 41 * q^54 + 14 * q^55 + 3 * q^56 - 7 * q^57 - 90 * q^58 + 15 * q^59 - 69 * q^60 - 56 * q^61 + 66 * q^62 + 13 * q^63 + 64 * q^64 - 21 * q^65 - 204 * q^66 - 26 * q^67 + 3 * q^68 + 58 * q^69 - 22 * q^70 - 63 * q^71 - 18 * q^72 - 22 * q^73 - 12 * q^74 + 118 * q^75 - 63 * q^76 - 69 * q^77 - 147 * q^78 - 2 * q^79 - 45 * q^80 + 29 * q^81 - 28 * q^82 - 51 * q^83 - 31 * q^84 - 10 * q^85 - 72 * q^86 - 67 * q^87 + 4 * q^88 + 132 * q^89 + 58 * q^90 - 13 * q^91 - 15 * q^92 + 217 * q^93 - 7 * q^94 - 21 * q^95 - 44 * q^96 + 3 * q^97 + 21 * q^98 - 148 * q^99

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.bn.a	$441$	$2$	441.bn	441.an	$42$	$648$	$54$	$3.521$		None		✓	✓	✓	441.2.bd.a	$2$	$0$	\(-21\)	\(-11\)	\(-18\)	\(-5\)		$\mathrm{SU}(2)[C_{42}]$