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

• Label: 6300.2.d
• Level: $6300$
• Weight: $2$
• Character orbit: 6300.d
• Rep. character: $\chi_{6300}(3401,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $6$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2880\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(11\), \(37\), \(41\)

Dimensions

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

	Total	New	Old
Modular forms	1512	52	1460
Cusp forms	1368	52	1316
Eisenstein series	144	0	144

Trace form

\( 52 q + 4 q^{7} + O(q^{10}) \)

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.d.a	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.b	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{7}+\beta _{1}q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.c	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{7}+\beta _{2}q^{11}+2\beta _{1}q^{13}+\cdots\)
6300.2.d.d	$6300$	$2$	6300.d	21.c	$2$	$12$	$12$	$50.306$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\beta _{1}q^{17}+\cdots\)
6300.2.d.e	$6300$	$2$	6300.d	21.c	$2$	$12$	$12$	$50.306$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{7}-\beta _{9}q^{11}-\beta _{8}q^{13}-\beta _{1}q^{17}+\cdots\)
6300.2.d.f	$6300$	$2$	6300.d	21.c	$2$	$16$	$16$	$50.306$	16.0.\(\cdots\).7	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}-\beta _{4}q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)