Space of modular forms of level 45, weight 3, and Character 45.i

• Label: 45.3.i
• Level: $45$
• Weight: $3$
• Character orbit: 45.i
• Rep. character: $\chi_{45}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	20	16	4
Eisenstein series	8	0	8

Trace form

16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9 - 18 * q^11 - 22 * q^12 - 10 * q^13 - 54 * q^14 + 10 * q^15 - 32 * q^16 - 8 * q^18 - 52 * q^19 + 72 * q^21 - 24 * q^22 - 54 * q^23 + 108 * q^24 + 40 * q^25 + 34 * q^27 + 32 * q^28 - 54 * q^29 - 100 * q^30 + 32 * q^31 + 216 * q^32 + 62 * q^33 + 54 * q^34 - 86 * q^36 + 44 * q^37 + 252 * q^38 + 160 * q^39 - 30 * q^40 + 144 * q^41 - 270 * q^42 - 124 * q^43 + 140 * q^45 - 108 * q^46 - 216 * q^47 - 172 * q^48 - 54 * q^49 - 106 * q^51 + 62 * q^52 - 316 * q^54 - 18 * q^56 - 236 * q^57 + 90 * q^58 - 486 * q^59 - 10 * q^60 + 62 * q^61 - 132 * q^63 + 256 * q^64 - 90 * q^65 + 208 * q^66 + 14 * q^67 - 288 * q^68 + 90 * q^69 - 60 * q^70 + 804 * q^72 - 268 * q^73 + 540 * q^74 - 20 * q^75 - 106 * q^76 + 702 * q^77 + 290 * q^78 - 40 * q^79 - 112 * q^81 - 204 * q^82 + 522 * q^83 + 714 * q^84 + 30 * q^85 + 54 * q^86 + 106 * q^87 + 144 * q^88 + 250 * q^90 + 136 * q^91 - 1332 * q^92 + 90 * q^93 - 150 * q^94 + 180 * q^95 + 166 * q^96 - 142 * q^97 - 824 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.3.i.a	$45$	$3$	45.i	9.d	$6$	$16$	$8$	$1.226$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	45.3.i.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(2\)	$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(-\beta _{7}+\beta _{11})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)