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

• Label: 30.8.e
• Level: $30$
• Weight: $8$
• Character orbit: 30.e
• Rep. character: $\chi_{30}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	92	28	64
Cusp forms	76	28	48
Eisenstein series	16	0	16

Trace form

28 * q - 52 * q^3 - 928 * q^6 - 1348 * q^7 - 416 * q^10 + 3328 * q^12 - 21840 * q^13 - 37672 * q^15 - 114688 * q^16 + 50624 * q^18 - 142744 * q^21 - 47008 * q^22 + 419744 * q^25 + 212972 * q^27 - 86272 * q^28 - 301152 * q^30 - 44936 * q^31 + 1398788 * q^33 + 50432 * q^36 + 608088 * q^37 + 339968 * q^40 - 624032 * q^42 - 1288968 * q^43 - 656648 * q^45 - 1486208 * q^46 + 212992 * q^48 + 4263064 * q^51 + 1397760 * q^52 - 3985428 * q^55 - 9921952 * q^57 - 416480 * q^58 - 365824 * q^60 - 14602248 * q^61 + 4050428 * q^63 + 10106816 * q^66 + 22755248 * q^67 + 551584 * q^70 - 3239936 * q^72 - 522380 * q^73 - 17815892 * q^75 - 4901888 * q^76 + 8835840 * q^78 + 33339556 * q^81 + 22502528 * q^82 + 27842408 * q^85 - 38505100 * q^87 - 3008512 * q^88 - 26143552 * q^90 - 77623680 * q^91 + 70200824 * q^93 + 3801088 * q^96 + 82948404 * q^97

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.e.a	$30$	$8$	30.e	15.e	$4$	$28$	$14$	$9.372$		None		✓	✓	✓	30.8.e.a	$4$	$0$	\(0\)	\(-52\)	\(0\)	\(-1348\)		$\mathrm{SU}(2)[C_{4}]$

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

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