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 - 4 * q^11 - 32 * q^14 + 56 * q^16 + 8 * q^19 + 12 * q^24 + 8 * q^26 + 16 * q^29 + 24 * q^31 + 8 * q^34 + 48 * q^36 - 56 * q^41 + 8 * q^44 - 48 * q^46 - 40 * q^49 + 16 * q^51 + 4 * q^54 - 96 * q^59 - 28 * q^61 - 32 * q^64 - 16 * q^66 - 16 * q^69 + 96 * q^71 + 168 * q^74 - 20 * q^76 - 24 * q^79 + 52 * q^81 + 32 * q^84 - 8 * q^86 + 32 * q^89 - 32 * q^94 - 68 * q^96 + 4 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1425.2.c.a	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					57.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}-3 i q^{7}+\cdots\)
1425.2.c.b	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					57.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+5 i q^{7}+\cdots\)
1425.2.c.c	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					285.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+2 i q^{7}+\cdots\)
1425.2.c.d	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					285.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}-2 i q^{7}+\cdots\)
1425.2.c.e	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		✓			1425.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}-4 i q^{7}+\cdots\)
1425.2.c.f	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					285.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+4 i q^{7}+\cdots\)
1425.2.c.g	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None					57.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+3 i q^{8}+\cdots\)
1425.2.c.h	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	\(\Q(\sqrt{-1}) \)	None		✓			1425.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+3 i q^{8}+\cdots\)
1425.2.c.i	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{7})\)	None					285.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{1}q^{3}-5q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1425.2.c.j	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{8})\)	None					285.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+\beta_1 q^{3}+(-2\beta_{3}-1)q^{4}+\cdots\)
1425.2.c.k	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{12})\)	None					285.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}+\beta_1 q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
1425.2.c.l	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(\zeta_{8})\)	None					285.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}-\beta_1 q^{3}+(-2\beta_{3}-1)q^{4}+\cdots\)
1425.2.c.m	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{5})\)	None		✓			1425.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1425.2.c.n	$1425$	$2$	1425.c	5.b	$2$	$4$	$4$	$11.379$	\(\Q(i, \sqrt{5})\)	None		✓			1425.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1425.2.c.o	$1425$	$2$	1425.c	5.b	$2$	$6$	$6$	$11.379$	6.0.44836416.1	None		✓			1425.2.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots\)
1425.2.c.p	$1425$	$2$	1425.c	5.b	$2$	$6$	$6$	$11.379$	6.0.24681024.1	None		✓			1425.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)