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

• Label: 1450.2.c
• Level: $1450$
• Weight: $2$
• Character orbit: 1450.c
• Rep. character: $\chi_{1450}(1101,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $450$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(450\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	238	48	190
Cusp forms	214	48	166
Eisenstein series	24	0	24

Trace form

48 * q - 48 * q^4 + 2 * q^6 + 4 * q^7 - 54 * q^9 + 6 * q^13 + 48 * q^16 + 2 * q^22 + 4 * q^23 - 2 * q^24 - 4 * q^28 - 12 * q^29 + 14 * q^33 + 32 * q^34 + 54 * q^36 + 20 * q^38 + 12 * q^42 + 48 * q^49 - 44 * q^51 - 6 * q^52 - 2 * q^53 - 38 * q^54 + 88 * q^57 - 24 * q^58 + 32 * q^59 - 10 * q^62 - 16 * q^63 - 48 * q^64 - 40 * q^71 + 64 * q^74 + 30 * q^78 + 32 * q^81 - 12 * q^82 - 28 * q^83 - 10 * q^86 + 12 * q^87 - 2 * q^88 - 12 * q^91 - 4 * q^92 + 34 * q^93 + 18 * q^94 + 2 * 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.c.a	$1450$	$2$	1450.c	29.b	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					58.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+2 q^{7}+\cdots\)
1450.2.c.b	$1450$	$2$	1450.c	29.b	$2$	$2$	$2$	$11.578$	\(\Q(\sqrt{-1}) \)	None					290.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-4 q^{7}-i q^{8}+3 q^{9}+\cdots\)
1450.2.c.c	$1450$	$2$	1450.c	29.b	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{29})\)	None					290.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
1450.2.c.d	$1450$	$2$	1450.c	29.b	$2$	$4$	$4$	$11.578$	\(\Q(i, \sqrt{5})\)	None					290.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)
1450.2.c.e	$1450$	$2$	1450.c	29.b	$2$	$10$	$10$	$11.578$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1450.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{5}q^{6}+\beta _{6}q^{7}+\cdots\)
1450.2.c.f	$1450$	$2$	1450.c	29.b	$2$	$10$	$10$	$11.578$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1450.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{5}q^{6}-\beta _{6}q^{7}+\cdots\)
1450.2.c.g	$1450$	$2$	1450.c	29.b	$2$	$16$	$16$	$11.578$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		290.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+(\beta _{7}-\beta _{8})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)