Space of modular forms of level 2900, weight 2, and Character 2900.d

• Label: 2900.2.d
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.d
• Rep. character: $\chi_{2900}(1101,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $900$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(900\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2900, [\chi])\).

	Total	New	Old
Modular forms	468	48	420
Cusp forms	432	48	384
Eisenstein series	36	0	36

Trace form

48 * q + 4 * q^7 - 42 * q^9 - 6 * q^13 + 4 * q^23 + 12 * q^29 + 14 * q^33 + 72 * q^49 + 16 * q^51 - 14 * q^53 - 20 * q^57 + 8 * q^59 + 8 * q^63 + 24 * q^67 + 20 * q^71 + 68 * q^81 - 52 * q^83 + 12 * q^87 - 24 * q^91 + 10 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(2900, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2900.2.d.a	$2900$	$2$	2900.d	29.b	$2$	$2$	$2$	$23.157$	\(\Q(\sqrt{-7}) \)	None					116.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+2q^{7}-4q^{9}+\beta q^{11}-5q^{13}+\cdots\)
2900.2.d.b	$2900$	$2$	2900.d	29.b	$2$	$2$	$2$	$23.157$	\(\Q(\sqrt{-7}) \)	None					580.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{7}+3q^{9}-\beta q^{11}+2q^{13}-\beta q^{19}+\cdots\)
2900.2.d.c	$2900$	$2$	2900.d	29.b	$2$	$4$	$4$	$23.157$	4.0.7168.1	None					580.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{3})q^{7}+(-3+2\beta _{3})q^{9}+\cdots\)
2900.2.d.d	$2900$	$2$	2900.d	29.b	$2$	$4$	$4$	$23.157$	\(\Q(\sqrt{-2}, \sqrt{11})\)	None					580.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(1-\beta _{3})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
2900.2.d.e	$2900$	$2$	2900.d	29.b	$2$	$10$	$10$	$23.157$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			2900.2.d.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{5}q^{7}+\beta _{2}q^{9}-\beta _{8}q^{11}+\cdots\)
2900.2.d.f	$2900$	$2$	2900.d	29.b	$2$	$10$	$10$	$23.157$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			2900.2.d.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{5}q^{7}+\beta _{2}q^{9}+\beta _{8}q^{11}+\cdots\)
2900.2.d.g	$2900$	$2$	2900.d	29.b	$2$	$16$	$16$	$23.157$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		580.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{8}q^{7}+(-2+\beta _{2})q^{9}+\beta _{14}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1450, [\chi])\)\(^{\oplus 2}\)