Space of modular forms of level 300, weight 2, and Character 300.j

• Label: 300.2.j
• Level: $300$
• Weight: $2$
• Character orbit: 300.j
• Rep. character: $\chi_{300}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).

	Total	New	Old
Modular forms	144	36	108
Cusp forms	96	36	60
Eisenstein series	48	0	48

Trace form

36 * q + 8 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 - 24 * q^16 + 20 * q^17 - 12 * q^22 - 32 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 - 8 * q^36 - 4 * q^37 - 16 * q^38 - 32 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 + 8 * q^56 + 20 * q^58 + 64 * q^61 + 56 * q^62 + 48 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 - 16 * q^76 - 48 * q^77 + 24 * q^78 - 36 * q^81 - 16 * q^82 - 8 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 32 * q^96 + 20 * q^97 - 24 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(300, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.2.j.a	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	\(\Q(\zeta_{24})\)	None		✓			300.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{5}-\beta_{4}+\beta_1)q^{2}+\beta_1 q^{3}+(\beta_{6}-\beta_{2})q^{4}+\cdots\)
300.2.j.b	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	8.0.157351936.1	None		✓			300.2.j.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\)
300.2.j.c	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	\(\Q(\zeta_{24})\)	None		✓			300.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_{7}-\beta_1)q^{2}-\beta_{5} q^{3}+(-\beta_{6}+\beta_{2})q^{4}+\cdots\)
300.2.j.d	$300$	$2$	300.j	20.e	$4$	$12$	$6$	$2.396$	12.0.\(\cdots\).1	None			✓		60.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

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