Properties

Label 832.2.w
Level $832$
Weight $2$
Character orbit 832.w
Rep. character $\chi_{832}(257,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $52$
Newform subspaces $10$
Sturm bound $224$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 832.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(832, [\chi])\).

Total New Old
Modular forms 248 60 188
Cusp forms 200 52 148
Eisenstein series 48 8 40

Trace form

\( 52 q - 24 q^{9} + O(q^{10}) \) \( 52 q - 24 q^{9} - 4 q^{13} - 6 q^{17} - 52 q^{25} + 2 q^{29} - 6 q^{33} + 6 q^{37} + 6 q^{41} - 24 q^{45} + 12 q^{49} + 8 q^{53} + 10 q^{61} + 20 q^{65} - 10 q^{69} + 36 q^{77} - 18 q^{81} - 24 q^{85} - 6 q^{89} + 12 q^{93} - 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
832.2.w.a 832.w 13.e $2$ $6.644$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+\cdots\)
832.2.w.b 832.w 13.e $2$ $6.644$ \(\Q(\sqrt{-3}) \) None 52.2.h.a \(0\) \(-1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.w.c 832.w 13.e $2$ $6.644$ \(\Q(\sqrt{-3}) \) None 52.2.h.a \(0\) \(1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.w.d 832.w 13.e $2$ $6.644$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
832.2.w.e 832.w 13.e $4$ $6.644$ \(\Q(\zeta_{12})\) None 416.2.w.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2-4\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
832.2.w.f 832.w 13.e $4$ $6.644$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) 416.2.w.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+3\zeta_{12}^{2}q^{9}+\cdots\)
832.2.w.g 832.w 13.e $8$ $6.644$ 8.0.195105024.2 None 104.2.o.a \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
832.2.w.h 832.w 13.e $8$ $6.644$ 8.0.56070144.2 None 416.2.w.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{3}+(\beta _{4}-\beta _{5})q^{5}-\beta _{3}q^{7}+(-2+\cdots)q^{9}+\cdots\)
832.2.w.i 832.w 13.e $8$ $6.644$ 8.0.195105024.2 None 104.2.o.a \(0\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
832.2.w.j 832.w 13.e $12$ $6.644$ 12.0.\(\cdots\).1 None 416.2.w.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{9}q^{3}+(2\beta _{4}+\beta _{5}-\beta _{6})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)