Space of Modular Forms of Level 3311, Weight 1, and Character 3311.h

• Label: 3311.1.h
• Level: 3311
• Weight: 1
• Character orbit: h
• Rep. character: \(\chi_{3311}(3310,\cdot)\)
• Character field: \(\Q\)
• Dimension: 38
• Newforms: 16
• Sturm bound: 352
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	=	\( 1 \)
Character orbit:	\([\chi]\)	=	3311.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 3311 \)
Character field:			\(\Q\)
Newforms:			\( 16 \)
Sturm bound:			\(352\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3311, [\chi])\).

	Total	New	Old
Modular forms	42	42	0
Cusp forms	38	38	0
Eisenstein series	4	4	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	38	0	0	0

Trace form

\( 38q + 30q^{4} + 26q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) into irreducible Hecke orbits

Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
							\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
3311.1.h.a	\(1\)	\(1.652\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3311}) \)	\(\Q(\sqrt{473}) \)	\(-2\)	\(0\)	\(0\)	\(-1\)	\(q-2q^{2}+3q^{4}-q^{7}-4q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.b	\(1\)	\(1.652\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-3311}) \)	None	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(q-q^{2}-q^{3}-q^{5}+q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.c	\(1\)	\(1.652\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-3311}) \)	None	\(-1\)	\(1\)	\(1\)	\(1\)	\(q-q^{2}+q^{3}+q^{5}-q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.d	\(1\)	\(1.652\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-3311}) \)	None	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(q+q^{2}-q^{3}-q^{5}-q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.e	\(1\)	\(1.652\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-3311}) \)	None	\(1\)	\(1\)	\(1\)	\(-1\)	\(q+q^{2}+q^{3}+q^{5}+q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.f	\(1\)	\(1.652\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3311}) \)	\(\Q(\sqrt{473}) \)	\(2\)	\(0\)	\(0\)	\(1\)	\(q+2q^{2}+3q^{4}+q^{7}+4q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.g	\(2\)	\(1.652\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	None	\(\Q(\sqrt{473}) \)	\(-2\)	\(0\)	\(0\)	\(-1\)	\(q-q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.h	\(2\)	\(1.652\)	\(\Q(\sqrt{3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3311}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(q-q^{2}-\beta q^{3}-\beta q^{5}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.i	\(2\)	\(1.652\)	\(\Q(\sqrt{3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3311}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(q+q^{2}-\beta q^{3}-\beta q^{5}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.j	\(2\)	\(1.652\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	None	\(\Q(\sqrt{473}) \)	\(2\)	\(0\)	\(0\)	\(1\)	\(q+q^{2}-\zeta_{6}^{2}q^{7}-q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.k	\(3\)	\(1.652\)	\(\Q(\zeta_{18})^+\)	\(D_{9}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(-3\)	\(q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3311.1.h.l	\(3\)	\(1.652\)	\(\Q(\zeta_{18})^+\)	\(D_{9}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(3\)	\(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
3311.1.h.m	\(3\)	\(1.652\)	\(\Q(\zeta_{18})^+\)	\(D_{9}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(-3\)	\(q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3311.1.h.n	\(3\)	\(1.652\)	\(\Q(\zeta_{18})^+\)	\(D_{9}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(3\)	\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
3311.1.h.o	\(6\)	\(1.652\)	\(\Q(\zeta_{36})^+\)	\(D_{18}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(-6\)	\(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
3311.1.h.p	\(6\)	\(1.652\)	\(\Q(\zeta_{36})^+\)	\(D_{18}\)	\(\Q(\sqrt{-3311}) \)	None	\(0\)	\(0\)	\(0\)	\(6\)	\(q+(\beta _{2}+\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4})q^{4}+\cdots\)