Space of modular forms of level 30, weight 8, and Character 30.c

• Label: 30.8.c
• Level: $30$
• Weight: $8$
• Character orbit: 30.c
• Rep. character: $\chi_{30}(19,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(30, [\chi])\).

	Total	New	Old
Modular forms	46	6	40
Cusp forms	38	6	32
Eisenstein series	8	0	8

Trace form

6 * q - 384 * q^4 + 164 * q^5 - 432 * q^6 - 4374 * q^9 - 1584 * q^10 - 18476 * q^11 + 8992 * q^14 + 24354 * q^15 + 24576 * q^16 - 60576 * q^19 - 10496 * q^20 - 91260 * q^21 + 27648 * q^24 - 85854 * q^25 + 323040 * q^26 - 411264 * q^29 - 78624 * q^30 - 44304 * q^31 + 902112 * q^34 + 84724 * q^35 + 279936 * q^36 - 291924 * q^39 + 101376 * q^40 + 1207660 * q^41 + 1182464 * q^44 - 119556 * q^45 - 1732032 * q^46 - 2138190 * q^49 - 1216576 * q^50 - 433620 * q^51 + 314928 * q^54 - 2897160 * q^55 - 575488 * q^56 - 5427620 * q^59 - 1558656 * q^60 + 10249404 * q^61 - 1572864 * q^64 + 6688668 * q^65 - 776736 * q^66 + 4463208 * q^69 - 8257344 * q^70 + 11304984 * q^71 - 7367072 * q^74 - 7075944 * q^75 + 3876864 * q^76 + 10233792 * q^79 + 671744 * q^80 + 3188646 * q^81 + 5840640 * q^84 + 2999964 * q^85 + 10121024 * q^86 - 28104868 * q^89 + 1154736 * q^90 - 18313608 * q^91 - 449664 * q^94 - 17704896 * q^95 - 1769472 * q^96 + 13469004 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(30, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
30.8.c.a	$30$	$8$	30.c	5.b	$2$	$2$	$2$	$9.372$	\(\Q(\sqrt{-1}) \)	None		✓			30.8.c.a	$2$	$0$	\(0\)	\(0\)	\(-100\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8 i q^{2}-27 i q^{3}-64 q^{4}+(275 i-50)q^{5}+\cdots\)
30.8.c.b	$30$	$8$	30.c	5.b	$2$	$4$	$4$	$9.372$	\(\Q(i, \sqrt{2641})\)	None		✓	✓		30.8.c.b	$2$	$0$	\(0\)	\(0\)	\(264\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-8\beta _{1}q^{2}-3^{3}\beta _{1}q^{3}-2^{6}q^{4}+(66+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(30, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)