Space of modular forms of level 6300, weight 2, and Character 6300.f

• Label: 6300.2.f
• Level: $6300$
• Weight: $2$
• Character orbit: 6300.f
• Rep. character: $\chi_{6300}(3149,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $2880$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6300.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2880\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(11\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6300, [\chi])\).

	Total	New	Old
Modular forms	1512	48	1464
Cusp forms	1368	48	1320
Eisenstein series	144	0	144

Trace form

\( 48 q - 4 q^{49} - 32 q^{79} - 68 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6300, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6300.2.f.a	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	None					1260.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.b	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	\(\Q(\zeta_{24})\)	None					252.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{7}+\beta_{5} q^{11}+(-2\beta_{3}-\beta_1)q^{13}+\cdots\)
6300.2.f.c	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	None					1260.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.d	$6300$	$2$	6300.f	105.g	$2$	$24$	$24$	$50.306$		None		✓	✓		6300.2.d.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(6300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 2}\)