Space of modular forms of level 30, weight 3, and Character 30.d

• Label: 30.3.d
• Level: $30$
• Weight: $3$
• Character orbit: 30.d
• Rep. character: $\chi_{30}(11,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(30, [\chi])\).

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

Trace form

4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 8 * q^12 - 40 * q^13 + 20 * q^15 + 16 * q^16 + 32 * q^18 + 32 * q^19 - 52 * q^21 + 48 * q^22 + 8 * q^24 - 20 * q^25 + 28 * q^27 - 16 * q^28 - 20 * q^30 + 32 * q^31 + 24 * q^33 - 96 * q^34 + 16 * q^36 - 88 * q^37 - 40 * q^39 - 128 * q^42 + 56 * q^43 + 20 * q^45 - 24 * q^46 + 16 * q^48 + 180 * q^49 + 72 * q^51 + 80 * q^52 + 140 * q^54 + 152 * q^57 - 40 * q^60 - 64 * q^61 - 256 * q^63 - 32 * q^64 + 48 * q^66 - 328 * q^67 - 132 * q^69 + 120 * q^70 - 64 * q^72 + 200 * q^73 - 20 * q^75 - 64 * q^76 + 40 * q^78 - 112 * q^79 + 28 * q^81 + 192 * q^82 + 104 * q^84 - 120 * q^85 + 240 * q^87 - 96 * q^88 - 80 * q^90 - 80 * q^91 + 32 * q^93 - 120 * q^94 - 16 * q^96 + 296 * q^97 - 192 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(30, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
30.3.d.a	$30$	$3$	30.d	3.b	$2$	$4$	$4$	$0.817$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓	✓	✓	30.3.d.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(30, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)