Space of modular forms of level 150, weight 3, and Character 150.d

• Label: 150.3.d
• Level: $150$
• Weight: $3$
• Character orbit: 150.d
• Rep. character: $\chi_{150}(101,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(150, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

12 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 - 8 * q^7 - 4 * q^9 + 8 * q^12 + 40 * q^13 + 48 * q^16 - 32 * q^18 - 44 * q^19 + 44 * q^21 - 48 * q^22 - 16 * q^24 - 28 * q^27 + 16 * q^28 - 124 * q^31 - 24 * q^33 + 112 * q^34 + 8 * q^36 + 88 * q^37 + 60 * q^39 + 128 * q^42 - 56 * q^43 - 32 * q^46 - 16 * q^48 + 120 * q^49 - 184 * q^51 - 80 * q^52 - 40 * q^54 - 152 * q^57 - 132 * q^61 + 256 * q^63 - 96 * q^64 - 176 * q^66 + 328 * q^67 + 224 * q^69 + 64 * q^72 - 200 * q^73 + 88 * q^76 - 40 * q^78 - 56 * q^79 + 284 * q^81 - 192 * q^82 - 88 * q^84 - 240 * q^87 + 96 * q^88 + 620 * q^91 - 32 * q^93 + 80 * q^94 + 32 * q^96 - 296 * q^97 - 656 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.3.d.a	$150$	$3$	150.d	3.b	$2$	$2$	$2$	$4.087$	\(\Q(\sqrt{-2}) \)	None		✓			150.3.d.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-14\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+(4-\beta )q^{6}+\cdots\)
150.3.d.b	$150$	$3$	150.d	3.b	$2$	$2$	$2$	$4.087$	\(\Q(\sqrt{-2}) \)	None		✓			150.3.d.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(1-2\beta )q^{3}-2q^{4}+(4+\beta )q^{6}+\cdots\)
150.3.d.c	$150$	$3$	150.d	3.b	$2$	$4$	$4$	$4.087$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None					30.3.d.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}-2q^{4}+\cdots\)
150.3.d.d	$150$	$3$	150.d	3.b	$2$	$4$	$4$	$4.087$	\(\Q(\sqrt{-2}, \sqrt{-17})\)	None					30.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(-1+\beta _{3})q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)