Space of modular forms of level 6600, weight 2, and Character 6600.d

• Label: 6600.2.d
• Level: $6600$
• Weight: $2$
• Character orbit: 6600.d
• Rep. character: $\chi_{6600}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $33$
• Sturm bound: $2880$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 6600 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6600.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 33 \)
Sturm bound:			\(2880\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6600, [\chi])\).

	Total	New	Old
Modular forms	1488	88	1400
Cusp forms	1392	88	1304
Eisenstein series	96	0	96

Trace form

\( 88 q - 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6600, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6600.2.d.a	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
6600.2.d.b	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+3iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
6600.2.d.c	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}+6iq^{17}+\cdots\)
6600.2.d.d	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}-4iq^{17}+\cdots\)
6600.2.d.e	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}-q^{11}-2iq^{13}-2iq^{17}+\cdots\)
6600.2.d.f	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}-q^{11}+2iq^{13}+\cdots\)
6600.2.d.g	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}-q^{11}+iq^{17}+\cdots\)
6600.2.d.h	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
6600.2.d.i	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+3iq^{7}-q^{9}-q^{11}-5iq^{13}+\cdots\)
6600.2.d.j	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}-iq^{13}+\cdots\)
6600.2.d.k	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}-q^{11}-2iq^{13}+\cdots\)
6600.2.d.l	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}+4iq^{13}+\cdots\)
6600.2.d.m	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}-q^{11}+2iq^{13}-6iq^{17}+\cdots\)
6600.2.d.n	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}-q^{11}-6iq^{13}+\cdots\)
6600.2.d.o	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+q^{11}-2iq^{17}+\cdots\)
6600.2.d.p	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}+q^{11}-4iq^{13}+\cdots\)
6600.2.d.q	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots\)
6600.2.d.r	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}+q^{11}-3iq^{17}+\cdots\)
6600.2.d.s	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{9}+q^{11}+2iq^{13}-6iq^{17}+\cdots\)
6600.2.d.t	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}+q^{11}+6iq^{13}-6iq^{17}+\cdots\)
6600.2.d.u	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}+q^{11}-6iq^{13}+\cdots\)
6600.2.d.v	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+q^{11}+4iq^{17}+\cdots\)
6600.2.d.w	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+q^{11}+4iq^{13}+\cdots\)
6600.2.d.x	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}+q^{11}+iq^{13}+\cdots\)
6600.2.d.y	$6600$	$2$	6600.d	5.b	$2$	$2$	$2$	$52.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}+q^{11}+8iq^{17}+\cdots\)
6600.2.d.z	$6600$	$2$	6600.d	5.b	$2$	$4$	$4$	$52.701$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{7}-q^{9}-q^{11}+(-2\zeta_{8}+\cdots)q^{13}+\cdots\)
6600.2.d.ba	$6600$	$2$	6600.d	5.b	$2$	$4$	$4$	$52.701$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}+3\beta _{2})q^{7}-q^{9}+q^{11}+\cdots\)
6600.2.d.bb	$6600$	$2$	6600.d	5.b	$2$	$4$	$4$	$52.701$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{7}-q^{9}+q^{11}+(-2\zeta_{8}+\cdots)q^{13}+\cdots\)
6600.2.d.bc	$6600$	$2$	6600.d	5.b	$2$	$4$	$4$	$52.701$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}-q^{9}+q^{11}+\cdots\)
6600.2.d.bd	$6600$	$2$	6600.d	5.b	$2$	$4$	$4$	$52.701$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+q^{11}+\cdots\)
6600.2.d.be	$6600$	$2$	6600.d	5.b	$2$	$6$	$6$	$52.701$	6.0.1351885824.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}-q^{11}+\cdots\)
6600.2.d.bf	$6600$	$2$	6600.d	5.b	$2$	$6$	$6$	$52.701$	6.0.27206656.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{2}q^{7}-q^{9}-q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)
6600.2.d.bg	$6600$	$2$	6600.d	5.b	$2$	$6$	$6$	$52.701$	6.0.65545216.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{7}-q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)