Space of modular forms of level 300, weight 11, and Character 300.k

• Label: 300.11.k
• Level: $300$
• Weight: $11$
• Character orbit: 300.k
• Rep. character: $\chi_{300}(157,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $660$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(660\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(300, [\chi])\).

	Total	New	Old
Modular forms	1236	60	1176
Cusp forms	1164	60	1104
Eisenstein series	72	0	72

Trace form

\( 60 q + 26180 q^{7} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(300, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.11.k.a	$300$	$11$	300.k	5.c	$4$	$12$	$6$	$190.607$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{6}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+3^{4}\beta _{3}q^{3}+(2496\beta _{1}+\beta _{6})q^{7}+3^{9}\beta _{2}q^{9}+\cdots\)
300.11.k.b	$300$	$11$	300.k	5.c	$4$	$12$	$6$	$190.607$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{18}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+3\beta _{7}q^{3}+(-109\beta _{2}+\beta _{6})q^{7}-3^{9}\beta _{1}q^{9}+\cdots\)
300.11.k.c	$300$	$11$	300.k	5.c	$4$	$16$	$8$	$190.607$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{44}\cdot 3^{12}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{4}]$	\(q+3^{4}\beta _{3}q^{3}+(-143\beta _{2}-\beta _{8})q^{7}-3^{9}\beta _{1}q^{9}+\cdots\)
300.11.k.d	$300$	$11$	300.k	5.c	$4$	$20$	$10$	$190.607$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(26180\)	$2^{48}\cdot 3^{36}\cdot 5^{26}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{3}+(1309+1309\beta _{1}+4\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)