Space of modular forms of level 1425, weight 2, and Character 1425.c

• Label: 1425.2.c
• Level: $1425$
• Weight: $2$
• Character orbit: 1425.c
• Rep. character: $\chi_{1425}(799,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $16$
• Sturm bound: $400$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1425.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(400\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

	Total	New	Old
Modular forms	212	52	160
Cusp forms	188	52	136
Eisenstein series	24	0	24

Trace form

\( 52 q - 48 q^{4} - 4 q^{6} - 52 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1425.2.c.a	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots\)
1425.2.c.b	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+5iq^{7}+\cdots\)
1425.2.c.c	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+2iq^{7}+\cdots\)
1425.2.c.d	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}-2iq^{7}+\cdots\)
1425.2.c.e	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
1425.2.c.f	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
1425.2.c.g	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)
1425.2.c.h	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)
1425.2.c.i	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{1}q^{3}-5q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1425.2.c.j	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1425.2.c.k	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{3}q^{6}+\cdots\)
1425.2.c.l	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1425.2.c.m	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1425.2.c.n	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1425.2.c.o	$1425$	$2$	1425.c	5.b	$2$	$6$	$6$	$11.379$	6.0.44836416.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots\)
1425.2.c.p	$1425$	$2$	1425.c	5.b	$2$	$6$	$6$	$11.379$	6.0.24681024.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \)