Space of modular forms of level 150, weight 8, and Character 150.e

• Label: 150.8.e
• Level: $150$
• Weight: $8$
• Character orbit: 150.e
• Rep. character: $\chi_{150}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $84$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(150, [\chi])\).

	Total	New	Old
Modular forms	444	84	360
Cusp forms	396	84	312
Eisenstein series	48	0	48

Trace form

84 * q + 52 * q^3 + 1856 * q^6 + 1348 * q^7 - 3328 * q^12 + 21840 * q^13 - 344064 * q^16 - 50624 * q^18 + 285488 * q^21 + 47008 * q^22 - 212972 * q^27 + 86272 * q^28 + 160392 * q^31 - 1398788 * q^33 - 100864 * q^36 - 608088 * q^37 + 624032 * q^42 + 1288968 * q^43 + 2972416 * q^46 - 212992 * q^48 - 4071548 * q^51 - 1397760 * q^52 + 9921952 * q^57 + 416480 * q^58 + 15677176 * q^61 - 4050428 * q^63 - 2473312 * q^66 - 22755248 * q^67 + 3239936 * q^72 + 522380 * q^73 - 2450944 * q^76 - 8835840 * q^78 - 1550672 * q^81 - 22502528 * q^82 + 38505100 * q^87 + 3008512 * q^88 + 111903360 * q^91 - 70200824 * q^93 - 7602176 * q^96 - 82948404 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.8.e.a	$150$	$8$	150.e	15.e	$4$	$16$	$8$	$46.858$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			150.8.e.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{52}\cdot 3^{16}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}+(2\beta _{7}+\beta _{9})q^{3}-2^{6}\beta _{2}q^{4}+\cdots\)
150.8.e.b	$150$	$8$	150.e	15.e	$4$	$28$	$14$	$46.858$		None					30.8.e.a	$4$	$0$	\(0\)	\(52\)	\(0\)	\(1348\)		$\mathrm{SU}(2)[C_{4}]$
150.8.e.c	$150$	$8$	150.e	15.e	$4$	$40$	$20$	$46.858$		None		✓	✓		150.8.e.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{8}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)