Properties

Label 3360.2.t
Level $3360$
Weight $2$
Character orbit 3360.t
Rep. character $\chi_{3360}(2689,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $14$
Sturm bound $1536$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(1536\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

Total New Old
Modular forms 800 72 728
Cusp forms 736 72 664
Eisenstein series 64 0 64

Trace form

\( 72 q + 8 q^{5} - 72 q^{9} + O(q^{10}) \) \( 72 q + 8 q^{5} - 72 q^{9} + 24 q^{25} - 16 q^{29} - 48 q^{41} - 8 q^{45} - 72 q^{49} + 16 q^{61} + 72 q^{81} + 16 q^{85} + 48 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3360.2.t.a $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}+iq^{7}-q^{9}+\cdots\)
3360.2.t.b $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}+(-2-i)q^{5}-iq^{7}-q^{9}+\cdots\)
3360.2.t.c $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+(1-2i)q^{5}-iq^{7}-q^{9}-6q^{11}+\cdots\)
3360.2.t.d $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-2i)q^{5}+iq^{7}-q^{9}-2q^{11}+\cdots\)
3360.2.t.e $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+2q^{11}+\cdots\)
3360.2.t.f $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+(1+2i)q^{5}-iq^{7}-q^{9}+6q^{11}+\cdots\)
3360.2.t.g $4$ $26.830$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+2\beta _{2}q^{13}+\cdots\)
3360.2.t.h $6$ $26.830$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3360.2.t.i $6$ $26.830$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3360.2.t.j $8$ $26.830$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}q^{7}-q^{9}+\cdots\)
3360.2.t.k $8$ $26.830$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{3}-\zeta_{24}^{6}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots\)
3360.2.t.l $8$ $26.830$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{3}-\zeta_{24}^{3}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots\)
3360.2.t.m $10$ $26.830$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
3360.2.t.n $10$ $26.830$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)