Properties

Label 3311.1.h
Level $3311$
Weight $1$
Character orbit 3311.h
Rep. character $\chi_{3311}(3310,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $16$
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: \(\Q\)
Newform subspaces: \( 16 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) into newform subspaces

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

Additional information

This newspace contains the most newforms of any with weight $1$ and level at most $4000$.