Space of modular forms of level 3900, weight 2, and Character 3900.h

• Label: 3900.2.h
• Level: $3900$
• Weight: $2$
• Character orbit: 3900.h
• Rep. character: $\chi_{3900}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $12$
• Sturm bound: $1680$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1680\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

	Total	New	Old
Modular forms	876	36	840
Cusp forms	804	36	768
Eisenstein series	72	0	72

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3900.2.h.a	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-6q^{11}-iq^{13}+\cdots\)
3900.2.h.b	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}-4q^{11}+iq^{13}+\cdots\)
3900.2.h.c	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-3q^{11}+iq^{13}+\cdots\)
3900.2.h.d	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots\)
3900.2.h.e	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}-iq^{13}-6iq^{17}+\cdots\)
3900.2.h.f	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}+q^{11}-iq^{13}+\cdots\)
3900.2.h.g	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}+q^{11}-iq^{13}+\cdots\)
3900.2.h.h	$3900$	$2$	3900.h	5.b	$2$	$2$	$2$	$31.142$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}+3q^{11}+iq^{13}+\cdots\)
3900.2.h.i	$3900$	$2$	3900.h	5.b	$2$	$4$	$4$	$31.142$	\(\Q(i, \sqrt{73})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(1-\beta _{3})q^{11}+\cdots\)
3900.2.h.j	$3900$	$2$	3900.h	5.b	$2$	$4$	$4$	$31.142$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+(2-\beta _{3})q^{11}+\cdots\)
3900.2.h.k	$3900$	$2$	3900.h	5.b	$2$	$6$	$6$	$31.142$	6.0.60217600.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5})q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
3900.2.h.l	$3900$	$2$	3900.h	5.b	$2$	$6$	$6$	$31.142$	6.0.146700544.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+(2-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)