Properties

Label 2015.1.h
Level $2015$
Weight $1$
Character orbit 2015.h
Rep. character $\chi_{2015}(2014,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $5$
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: \(\Q\)
Newform subspaces: \( 5 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2015.1.h.a 2015.h 2015.h $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-155}) \) 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 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) 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 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) 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 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) 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 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) None \(1\) \(1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)