Properties

Label 2015.1.bq
Level $2015$
Weight $1$
Character orbit 2015.bq
Rep. character $\chi_{2015}(464,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{6})\)
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 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 8 0 0

Trace form

\( 16 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{4} - 4 q^{9} - 4 q^{10} - 8 q^{14} + 4 q^{19} - 8 q^{31} - 4 q^{35} - 4 q^{36} + 12 q^{39} + 8 q^{40} + 8 q^{41} - 8 q^{45} - 4 q^{49} - 16 q^{51} + 4 q^{56} + 8 q^{59} + 8 q^{66} + 4 q^{71} - 8 q^{81} + 4 q^{95} + O(q^{100}) \)

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.bq.a 2015.bq 2015.aq $2$ $1.006$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-155}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.b 2015.bq 2015.aq $2$ $1.006$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-155}) \) None \(0\) \(2\) \(2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.c 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2015.1.bq.d 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\)
2015.1.bq.e 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)