Space of modular forms of level 1450, weight 2, and Character 1450.d

• Label: 1450.2.d
• Level: $1450$
• Weight: $2$
• Character orbit: 1450.d
• Rep. character: $\chi_{1450}(1449,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $10$
• Sturm bound: $450$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(450\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

	Total	New	Old
Modular forms	236	44	192
Cusp forms	212	44	168
Eisenstein series	24	0	24

Trace form

44 * q + 44 * q^4 + 12 * q^6 + 48 * q^9 + 44 * q^16 + 12 * q^24 + 8 * q^29 - 24 * q^34 + 48 * q^36 - 52 * q^49 + 48 * q^51 + 36 * q^54 + 44 * q^59 + 44 * q^64 + 24 * q^71 - 4 * q^74 + 124 * q^81 + 12 * q^86 + 48 * q^91 + 8 * q^94 + 12 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1450.2.d.a	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					290.2.c.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+2\beta q^{7}-q^{8}-3 q^{9}+\cdots\)
1450.2.d.b	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					58.2.b.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2 i q^{7}+\cdots\)
1450.2.d.c	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					58.2.b.a	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+2 i q^{7}+\cdots\)
1450.2.d.d	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					290.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+2\beta q^{7}+q^{8}-3 q^{9}+\cdots\)
1450.2.d.e	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{5})\)	None					290.2.c.c	$2$	$0$	\(-4\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)
1450.2.d.f	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{29})\)	None					290.2.c.b	$2$	$0$	\(-4\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
1450.2.d.g	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{29})\)	None					290.2.c.b	$2$	$0$	\(4\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
1450.2.d.h	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{5})\)	None					290.2.c.c	$2$	$0$	\(4\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(1-\beta _{2})q^{6}+\cdots\)
1450.2.d.i	$1450$	$2$	1450.d	145.d	$2$	$10$	$10$	$11.578$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1450.2.c.e	$2$	$0$	\(-10\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{5}q^{3}+q^{4}-\beta _{5}q^{6}+\beta _{2}q^{7}+\cdots\)
1450.2.d.j	$1450$	$2$	1450.d	145.d	$2$	$10$	$10$	$11.578$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1450.2.c.e	$2$	$0$	\(10\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{5}q^{3}+q^{4}-\beta _{5}q^{6}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)