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

• Label: 2600.2.d
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.d
• Rep. character: $\chi_{2600}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $16$
• Sturm bound: $840$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2600.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(840\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	444	54	390
Cusp forms	396	54	342
Eisenstein series	48	0	48

Trace form

\( 54 q - 46 q^{9} - 12 q^{11} + 12 q^{19} + 24 q^{21} - 24 q^{29} + 8 q^{31} + 8 q^{41} - 6 q^{49} + 24 q^{51} + 8 q^{59} - 24 q^{61} + 24 q^{69} - 16 q^{79} + 38 q^{81} - 32 q^{89} - 12 q^{91} + 24 q^{99}+O(q^{100}) \)

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.d.a	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None		✓			2600.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-2 i q^{7}-6 q^{9}-2 q^{11}+\cdots\)
2600.2.d.b	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None		✓			2600.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+3 i q^{7}-q^{9}+q^{11}+i q^{13}+\cdots\)
2600.2.d.c	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None					520.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}-q^{9}+2 q^{11}+i q^{13}-2 i q^{17}+\cdots\)
2600.2.d.d	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None		✓			2600.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}-3 i q^{7}-q^{9}+3 q^{11}+\cdots\)
2600.2.d.e	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None		✓			2600.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{9}-2 q^{11}-i q^{13}-2 i q^{17}+\cdots\)
2600.2.d.f	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None					104.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-5 i q^{7}+2 q^{9}-2 q^{11}+\cdots\)
2600.2.d.g	$2600$	$2$	2600.d	5.b	$2$	$2$	$2$	$20.761$	\(\Q(\sqrt{-1}) \)	None					520.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 q^{9}-4 q^{11}+i q^{13}-6 i q^{17}+\cdots\)
2600.2.d.h	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{6})\)	None					520.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-2\beta _{1}q^{7}-3q^{9}+(-2-\beta _{3})q^{11}+\cdots\)
2600.2.d.i	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(\zeta_{8})\)	None					520.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+2\beta_1)q^{3}-2\beta_1 q^{7}+(4\beta_{3}-3)q^{9}+\cdots\)
2600.2.d.j	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{5})\)	None					520.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(-3+2\beta _{3})q^{9}+\cdots\)
2600.2.d.k	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{17})\)	None					104.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+(-2+\cdots)q^{11}+\cdots\)
2600.2.d.l	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(\zeta_{12})\)	None					520.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}-2\beta_{2} q^{7}+(2\beta_{3}-1)q^{9}+\cdots\)
2600.2.d.m	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(\zeta_{12})\)	None					520.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}+2\beta_{2} q^{7}+(2\beta_{3}-1)q^{9}+\cdots\)
2600.2.d.n	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{73})\)	None		✓			2600.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+2q^{9}+(-1+\beta _{3})q^{11}+\beta _{2}q^{13}+\cdots\)
2600.2.d.o	$2600$	$2$	2600.d	5.b	$2$	$4$	$4$	$20.761$	\(\Q(i, \sqrt{10})\)	None		✓			2600.2.a.r	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{7}+3q^{9}+(3+\beta _{3})q^{11}+\cdots\)
2600.2.d.p	$2600$	$2$	2600.d	5.b	$2$	$8$	$8$	$20.761$	8.0.\(\cdots\).21	None		✓	✓		2600.2.a.z	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(\beta _{2}-\beta _{7})q^{7}+(-2-\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)