Properties

Label 2015.1.h
Level 2015
Weight 1
Character orbit h
Rep. character \(\chi_{2015}(2014,\cdot)\)
Character field \(\Q\)
Dimension 28
Newforms 5
Sturm bound 224
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2015.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2015 \)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2015, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 28 28 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 28 0 0 0

Trace form

\(28q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 16q^{56} \) \(\mathstrut +\mathstrut 8q^{64} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2015, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2015.1.h.a \(4\) \(1.006\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots\)
2015.1.h.b \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(-1\) \(-1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.c \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(-1\) \(1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.d \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(1\) \(-1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.h.e \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(1\) \(1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)