Properties

Label 2646.2.h
Level $2646$
Weight $2$
Character orbit 2646.h
Rep. character $\chi_{2646}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $20$
Sturm bound $1008$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

Total New Old
Modular forms 1104 80 1024
Cusp forms 912 80 832
Eisenstein series 192 0 192

Trace form

\( 80 q - 40 q^{4} + 8 q^{5} + O(q^{10}) \) \( 80 q - 40 q^{4} + 8 q^{5} - 16 q^{11} - 2 q^{13} - 40 q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{23} + 80 q^{25} - 16 q^{26} - 18 q^{29} - 2 q^{31} - 2 q^{37} + 24 q^{38} - 6 q^{41} - 2 q^{43} + 8 q^{44} + 6 q^{46} - 6 q^{47} + 4 q^{52} + 32 q^{53} + 12 q^{55} + 12 q^{58} - 22 q^{59} - 8 q^{61} + 44 q^{62} + 80 q^{64} + 2 q^{65} - 14 q^{67} + 28 q^{68} + 76 q^{71} + 28 q^{73} + 12 q^{74} + 4 q^{76} - 32 q^{79} - 4 q^{80} + 16 q^{83} - 24 q^{85} - 40 q^{86} - 36 q^{89} + 2 q^{92} - 12 q^{94} + 42 q^{95} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2646.2.h.a $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+q^{8}+\cdots\)
2646.2.h.b $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+q^{8}+\cdots\)
2646.2.h.c $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+q^{8}+\cdots\)
2646.2.h.d $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+q^{8}+\cdots\)
2646.2.h.e $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+q^{8}+\cdots\)
2646.2.h.f $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-6\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-q^{8}+\cdots\)
2646.2.h.g $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.h.h $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{8}+3q^{11}+\cdots\)
2646.2.h.i $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{8}+3q^{11}+\cdots\)
2646.2.h.j $2$ $21.128$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.h.k $4$ $21.128$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(-6\) \(0\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
2646.2.h.l $4$ $21.128$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(6\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2646.2.h.m $4$ $21.128$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2646.2.h.n $4$ $21.128$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(0\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2646.2.h.o $6$ $21.128$ 6.0.309123.1 None \(-3\) \(0\) \(-2\) \(0\) \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+\beta _{3}q^{5}+q^{8}+\cdots\)
2646.2.h.p $6$ $21.128$ 6.0.309123.1 None \(3\) \(0\) \(10\) \(0\) \(q+(1-\beta _{4})q^{2}-\beta _{4}q^{4}+(2+\beta _{1})q^{5}+\cdots\)
2646.2.h.q $8$ $21.128$ \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{24})q^{2}-\zeta_{24}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
2646.2.h.r $8$ $21.128$ 8.0.\(\cdots\).2 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
2646.2.h.s $8$ $21.128$ 8.0.3317760000.3 None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
2646.2.h.t $8$ $21.128$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{24})q^{2}-\zeta_{24}q^{4}+(-2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)