Properties

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

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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

\( 38q + 30q^{4} + 26q^{9} + O(q^{10}) \) \( 38q + 30q^{4} + 26q^{9} - 6q^{11} - 2q^{14} - 8q^{15} + 22q^{16} + 26q^{25} + 18q^{36} - 6q^{44} + 32q^{49} - 8q^{53} - 10q^{56} - 12q^{58} - 24q^{60} + 26q^{64} - 8q^{67} - 16q^{78} + 30q^{81} - 12q^{92} - 2q^{99} + O(q^{100}) \)

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 \(0\) \(0\) \(0\) \(6\) \(q+(\beta _{2}+\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4})q^{4}+\cdots\)