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

• Label: 6300.2.ch
• Level: $6300$
• Weight: $2$
• Character orbit: 6300.ch
• Rep. character: $\chi_{6300}(1601,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $6$
• Sturm bound: $2880$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6300.ch (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2880\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	3024	100	2924
Cusp forms	2736	100	2636
Eisenstein series	288	0	288

Trace form

\( 100 q - 6 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6300.2.ch.a	$6300$	$2$	6300.ch	21.g	$6$	$4$	$2$	$50.306$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+3\beta _{1})q^{7}+(\beta _{2}+\beta _{3})q^{11}+(1+\cdots)q^{13}+\cdots\)
6300.2.ch.b	$6300$	$2$	6300.ch	21.g	$6$	$12$	$6$	$50.306$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{7}+(-2-\beta _{1}-\beta _{4}+\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots\)
6300.2.ch.c	$6300$	$2$	6300.ch	21.g	$6$	$12$	$6$	$50.306$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{7}+(1-\beta _{2}-\beta _{4}-\beta _{6}+\beta _{7}+\cdots)q^{11}+\cdots\)
6300.2.ch.d	$6300$	$2$	6300.ch	21.g	$6$	$20$	$10$	$50.306$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5})q^{7}+(-\beta _{10}+\beta _{12})q^{11}+\cdots\)
6300.2.ch.e	$6300$	$2$	6300.ch	21.g	$6$	$20$	$10$	$50.306$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{5})q^{7}+(-\beta _{10}+\beta _{12})q^{11}+\cdots\)
6300.2.ch.f	$6300$	$2$	6300.ch	21.g	$6$	$32$	$16$	$50.306$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 2}\)