Space of modular forms of level 45, weight 4, and Character 45.b

• Label: 45.4.b
• Level: $45$
• Weight: $4$
• Character orbit: 45.b
• Rep. character: $\chi_{45}(19,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(45, [\chi])\).

	Total	New	Old
Modular forms	22	8	14
Cusp forms	14	6	8
Eisenstein series	8	2	6

Trace form

6 * q - 12 * q^4 - 6 * q^5 - 36 * q^10 + 84 * q^11 - 228 * q^14 - 12 * q^16 + 216 * q^19 + 396 * q^20 + 6 * q^25 + 12 * q^26 - 636 * q^29 - 360 * q^31 - 96 * q^34 + 300 * q^35 - 132 * q^40 + 816 * q^41 - 1116 * q^44 + 624 * q^46 + 546 * q^49 + 696 * q^50 - 864 * q^55 - 60 * q^56 - 372 * q^59 - 36 * q^61 - 108 * q^64 - 948 * q^65 + 1080 * q^70 + 72 * q^71 + 3132 * q^74 - 1464 * q^76 - 1368 * q^79 - 444 * q^80 + 2592 * q^85 - 4296 * q^86 + 2232 * q^89 + 1944 * q^91 + 792 * q^94 - 2784 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.4.b.a	$45$	$4$	45.b	5.b	$2$	$2$	$2$	$2.655$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		✓			45.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+3q^{4}+5\beta q^{5}+11\beta q^{8}-5^{2}q^{10}+\cdots\)
45.4.b.b	$45$	$4$	45.b	5.b	$2$	$4$	$4$	$2.655$	\(\Q(i, \sqrt{41})\)	None			✓		15.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)