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

• Label: 2900.2.s
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.s
• Rep. character: $\chi_{2900}(157,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $90$
• Newform subspaces: $5$
• Sturm bound: $900$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(900\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	936	90	846
Cusp forms	864	90	774
Eisenstein series	72	0	72

Trace form

90 * q + 74 * q^9 + 8 * q^11 + 6 * q^13 + 8 * q^21 - 12 * q^27 + 8 * q^31 - 4 * q^33 + 24 * q^37 + 24 * q^39 + 10 * q^41 + 16 * q^43 + 32 * q^47 + 18 * q^53 - 24 * q^57 + 14 * q^61 - 24 * q^63 - 16 * q^67 + 16 * q^69 + 40 * q^79 + 10 * q^81 - 56 * q^83 - 48 * q^87 - 18 * q^89 - 44 * q^93 + 16 * q^97

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.s.a	$2900$	$2$	2900.s	145.e	$4$	$2$	$1$	$23.157$	\(\Q(\sqrt{-1}) \)	None		✓			2900.2.j.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-2 q^{3}+(3 i+3)q^{7}+q^{9}+(2 i+2)q^{11}+\cdots\)
2900.2.s.b	$2900$	$2$	2900.s	145.e	$4$	$2$	$1$	$23.157$	\(\Q(\sqrt{-1}) \)	None		✓			2900.2.j.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2 q^{3}+(-3 i-3)q^{7}+q^{9}+(2 i+2)q^{11}+\cdots\)
2900.2.s.c	$2900$	$2$	2900.s	145.e	$4$	$16$	$8$	$23.157$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			2900.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{3}+\beta _{14}q^{7}+(1-\beta _{3})q^{9}+\beta _{10}q^{11}+\cdots\)
2900.2.s.d	$2900$	$2$	2900.s	145.e	$4$	$30$	$15$	$23.157$		None					580.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
2900.2.s.e	$2900$	$2$	2900.s	145.e	$4$	$40$	$20$	$23.157$		None		✓	✓		2900.2.j.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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