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

• Label: 2900.2.f
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.f
• Rep. character: $\chi_{2900}(1449,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $5$
• Sturm bound: $900$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(900\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	468	44	424
Cusp forms	432	44	388
Eisenstein series	36	0	36

Trace form

\( 44 q + 24 q^{9} - 4 q^{29} - 76 q^{49} - 36 q^{51} + 20 q^{59} + 12 q^{71} - 20 q^{81} - 12 q^{91}+O(q^{100}) \)

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.f.a	$2900$	$2$	2900.f	145.d	$2$	$4$	$4$	$23.157$	\(\Q(i, \sqrt{7})\)	None					580.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{7}-3q^{9}-\beta _{3}q^{11}-\beta _{1}q^{13}+\cdots\)
2900.2.f.b	$2900$	$2$	2900.f	145.d	$2$	$4$	$4$	$23.157$	\(\Q(i, \sqrt{7})\)	None					116.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-2\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots\)
2900.2.f.c	$2900$	$2$	2900.f	145.d	$2$	$8$	$8$	$23.157$	8.0.959512576.1	None					580.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-\beta _{2}+\beta _{3})q^{7}-q^{9}-\beta _{1}q^{11}+\cdots\)
2900.2.f.d	$2900$	$2$	2900.f	145.d	$2$	$8$	$8$	$23.157$	8.0.205520896.4	None					580.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(3-2\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.f.e	$2900$	$2$	2900.f	145.d	$2$	$20$	$20$	$23.157$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		2900.2.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{14}q^{7}-\beta _{4}q^{9}+(\beta _{10}-\beta _{13}+\cdots)q^{11}+\cdots\)

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

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