Properties

Label 3264.2.l
Level $3264$
Weight $2$
Character orbit 3264.l
Rep. character $\chi_{3264}(2209,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3264.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3264, [\chi])\).

Total New Old
Modular forms 600 72 528
Cusp forms 552 72 480
Eisenstein series 48 0 48

Trace form

\( 72 q + 72 q^{9} + O(q^{10}) \) \( 72 q + 72 q^{9} + 24 q^{17} + 24 q^{25} - 72 q^{49} + 72 q^{81} - 48 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3264, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3264.2.l.a 3264.l 136.h $4$ $26.063$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{8}^{2}q^{5}+q^{9}-4q^{11}+\zeta_{8}^{2}q^{15}+\cdots\)
3264.2.l.b 3264.l 136.h $4$ $26.063$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\zeta_{8}^{2}q^{5}+q^{9}+4q^{11}-\zeta_{8}^{2}q^{15}+\cdots\)
3264.2.l.c 3264.l 136.h $8$ $26.063$ 8.0.303595776.1 None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\)
3264.2.l.d 3264.l 136.h $8$ $26.063$ 8.0.303595776.1 None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+q^{9}+\cdots\)
3264.2.l.e 3264.l 136.h $24$ $26.063$ None \(0\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3264.2.l.f 3264.l 136.h $24$ $26.063$ None \(0\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1632, [\chi])\)\(^{\oplus 2}\)