Space of modular forms of level 300, weight 3, and Character 300.c

• Label: 300.3.c
• Level: $300$
• Weight: $3$
• Character orbit: 300.c
• Rep. character: $\chi_{300}(151,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $7$
• Sturm bound: $180$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(180\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(300, [\chi])\).

	Total	New	Old
Modular forms	132	38	94
Cusp forms	108	38	70
Eisenstein series	24	0	24

Trace form

38 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 + 4 * q^8 - 114 * q^9 + 12 * q^12 - 20 * q^13 + 52 * q^14 + 20 * q^16 - 20 * q^17 + 6 * q^18 + 24 * q^21 - 92 * q^22 - 36 * q^24 - 16 * q^26 - 76 * q^28 - 12 * q^29 + 108 * q^32 + 24 * q^33 + 164 * q^34 + 24 * q^36 + 60 * q^37 - 32 * q^38 - 116 * q^41 - 84 * q^42 + 64 * q^46 - 96 * q^48 - 234 * q^49 + 136 * q^52 - 204 * q^53 + 18 * q^54 - 472 * q^56 - 72 * q^57 + 152 * q^58 + 156 * q^61 + 32 * q^62 + 316 * q^64 - 168 * q^66 + 224 * q^68 - 96 * q^69 - 12 * q^72 + 332 * q^73 + 332 * q^74 + 240 * q^76 + 192 * q^77 + 228 * q^78 + 342 * q^81 + 76 * q^82 - 24 * q^84 - 76 * q^86 - 140 * q^88 - 132 * q^89 - 336 * q^92 - 120 * q^93 - 208 * q^94 + 156 * q^96 - 436 * q^97 - 658 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(300, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.3.c.a	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	\(\Q(\sqrt{-3}) \)	None					60.3.f.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta-1)q^{2}+\beta q^{3}+(2\beta-2)q^{4}+\cdots\)
300.3.c.b	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	\(\Q(\sqrt{-3}) \)	None					12.3.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{2}-\beta q^{3}+(2\beta-2)q^{4}+\cdots\)
300.3.c.c	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	\(\Q(\sqrt{-3}) \)	None					60.3.f.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{2}-\beta q^{3}+(2\beta-2)q^{4}+\cdots\)
300.3.c.d	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.85100625.1	None					60.3.c.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.e	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	None		✓			300.3.c.e	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.f	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.6080256576.2	None					60.3.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.g	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	None		✓			300.3.c.e	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(300, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)