Space of modular forms of level 2600, weight 2, and Character 2600.k

• Label: 2600.2.k
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.k
• Rep. character: $\chi_{2600}(2001,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $6$
• Sturm bound: $840$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2600.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(840\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2600, [\chi])\).

	Total	New	Old
Modular forms	444	66	378
Cusp forms	396	66	330
Eisenstein series	48	0	48

Trace form

\( 66 q - 2 q^{3} + 64 q^{9} + 2 q^{13} + 2 q^{17} - 12 q^{23} - 2 q^{27} - 20 q^{29} - 4 q^{39} + 30 q^{43} - 44 q^{49} - 2 q^{51} - 8 q^{53} - 4 q^{61} - 36 q^{69} - 36 q^{79} + 82 q^{81} + 16 q^{87} - 22 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2600, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2600.2.k.a	$2600$	$2$	2600.k	13.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{17})\)	None					104.2.f.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
2600.2.k.b	$2600$	$2$	2600.k	13.b	$2$	$6$	$6$	$20.761$	6.0.350464.1	None					520.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
2600.2.k.c	$2600$	$2$	2600.k	13.b	$2$	$8$	$8$	$20.761$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					520.2.k.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{2}-\beta _{4}+\beta _{5})q^{7}+(2+\cdots)q^{9}+\cdots\)
2600.2.k.d	$2600$	$2$	2600.k	13.b	$2$	$14$	$14$	$20.761$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			2600.2.k.d	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{7}q^{7}+(1-\beta _{1})q^{9}+(-\beta _{7}+\cdots)q^{11}+\cdots\)
2600.2.k.e	$2600$	$2$	2600.k	13.b	$2$	$14$	$14$	$20.761$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			2600.2.k.d	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{7}q^{7}+(1-\beta _{1})q^{9}+(-\beta _{7}+\cdots)q^{11}+\cdots\)
2600.2.k.f	$2600$	$2$	2600.k	13.b	$2$	$20$	$20$	$20.761$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None			✓		520.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{3}+\beta _{9}q^{7}+(1+\beta _{1})q^{9}+\beta _{18}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)