Properties

Label 4608.2.c
Level $4608$
Weight $2$
Character orbit 4608.c
Rep. character $\chi_{4608}(4607,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $18$
Sturm bound $1536$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 4608 = 2^{9} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4608.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1536\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4608, [\chi])\).

Total New Old
Modular forms 832 64 768
Cusp forms 704 64 640
Eisenstein series 128 0 128

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 64 q^{25} - 64 q^{49} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4608.2.c.a 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta q^{7}-4q^{11}-6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.b 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta q^{7}-4q^{11}+6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.c 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{5}+\beta q^{7}-2q^{13}-\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.d 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{5}-\beta q^{7}-2q^{13}-\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.e 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{5}-\beta q^{7}+2q^{13}+\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.f 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{5}+\beta q^{7}+2q^{13}+\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.g 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta q^{7}+4q^{11}-6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.h 4608.c 12.b $2$ $36.795$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta q^{7}+4q^{11}+6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.i 4608.c 12.b $4$ $36.795$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.j 4608.c 12.b $4$ $36.795$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.k 4608.c 12.b $4$ $36.795$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.l 4608.c 12.b $4$ $36.795$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.m 4608.c 12.b $4$ $36.795$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.n 4608.c 12.b $4$ $36.795$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.o 4608.c 12.b $4$ $36.795$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.p 4608.c 12.b $4$ $36.795$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.q 4608.c 12.b $8$ $36.795$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)
4608.2.c.r 4608.c 12.b $8$ $36.795$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4608, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)