Properties

Label 3360.2.j
Level $3360$
Weight $2$
Character orbit 3360.j
Rep. character $\chi_{3360}(1009,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $6$
Sturm bound $1536$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1536\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(13\)

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

\( 72 q + 72 q^{9} + O(q^{10}) \) \( 72 q + 72 q^{9} - 8 q^{25} - 16 q^{31} - 32 q^{39} + 16 q^{41} - 72 q^{49} - 32 q^{55} + 48 q^{65} + 64 q^{79} + 72 q^{81} + 80 q^{89} + 80 q^{95} + O(q^{100}) \)

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.j.a $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q-q^{3}+(-2+i)q^{5}-iq^{7}+q^{9}-6q^{13}+\cdots\)
3360.2.j.b $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) \(q-q^{3}+(2-i)q^{5}+iq^{7}+q^{9}+4iq^{11}+\cdots\)
3360.2.j.c $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+q^{3}+(-2-i)q^{5}-iq^{7}+q^{9}+4iq^{11}+\cdots\)
3360.2.j.d $2$ $26.830$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) \(q+q^{3}+(2+i)q^{5}+iq^{7}+q^{9}+6q^{13}+\cdots\)
3360.2.j.e $32$ $26.830$ None \(0\) \(-32\) \(0\) \(0\)
3360.2.j.f $32$ $26.830$ None \(0\) \(32\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)