Space of modular forms of level 30, weight 4, and Character 30.c

• Label: 30.4.c
• Level: $30$
• Weight: $4$
• Character orbit: 30.c
• Rep. character: $\chi_{30}(19,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(30, [\chi])\).

	Total	New	Old
Modular forms	22	2	20
Cusp forms	14	2	12
Eisenstein series	8	0	8

Trace form

2 * q - 8 * q^4 + 4 * q^5 - 12 * q^6 - 18 * q^9 - 44 * q^10 + 140 * q^11 + 8 * q^14 - 66 * q^15 + 32 * q^16 - 48 * q^19 - 16 * q^20 + 12 * q^21 + 48 * q^24 - 234 * q^25 + 216 * q^26 - 432 * q^29 - 24 * q^30 + 416 * q^31 + 88 * q^34 + 44 * q^35 + 72 * q^36 + 324 * q^39 + 176 * q^40 - 412 * q^41 - 560 * q^44 - 36 * q^45 - 400 * q^46 + 678 * q^49 - 176 * q^50 + 132 * q^51 + 108 * q^54 + 280 * q^55 - 32 * q^56 + 740 * q^59 + 264 * q^60 - 1100 * q^61 - 128 * q^64 + 1188 * q^65 - 840 * q^66 - 600 * q^69 + 16 * q^70 - 1080 * q^71 + 1016 * q^74 - 264 * q^75 + 192 * q^76 - 1584 * q^79 + 64 * q^80 + 162 * q^81 - 48 * q^84 + 484 * q^85 + 1168 * q^86 + 1876 * q^89 + 396 * q^90 - 216 * q^91 + 1280 * q^94 - 96 * q^95 - 192 * q^96 - 1260 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(30, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
30.4.c.a	$30$	$4$	30.c	5.b	$2$	$2$	$2$	$1.770$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	30.4.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+3 i q^{3}-4 q^{4}+(11 i+2)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(30, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)