Properties

Label 832.2.k
Level $832$
Weight $2$
Character orbit 832.k
Rep. character $\chi_{832}(255,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $52$
Newform subspaces $10$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 832.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(11\)

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

\( 52 q + 4 q^{5} - 52 q^{9} + O(q^{10}) \) \( 52 q + 4 q^{5} - 52 q^{9} + 4 q^{13} + 8 q^{21} + 8 q^{29} + 8 q^{33} - 12 q^{37} - 12 q^{41} + 12 q^{45} + 8 q^{53} + 8 q^{57} + 8 q^{61} - 12 q^{65} - 12 q^{73} + 36 q^{81} - 16 q^{85} + 4 q^{89} - 72 q^{93} + 4 q^{97} + O(q^{100}) \)

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.k.a 832.k 52.f $2$ $6.644$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 208.2.k.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i-1)q^{5}+3 q^{9}+(-3 i-2)q^{13}+\cdots\)
832.2.k.b 832.k 52.f $2$ $6.644$ \(\Q(\sqrt{-1}) \) None 416.2.k.a \(0\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+2 i q^{3}+(i+1)q^{5}+(-i-1)q^{7}+\cdots\)
832.2.k.c 832.k 52.f $2$ $6.644$ \(\Q(\sqrt{-1}) \) None 416.2.k.a \(0\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q-2 i q^{3}+(i+1)q^{5}+(i+1)q^{7}+\cdots\)
832.2.k.d 832.k 52.f $2$ $6.644$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 52.2.f.a \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(3 i+3)q^{5}+3 q^{9}+(-3 i+2)q^{13}+\cdots\)
832.2.k.e 832.k 52.f $4$ $6.644$ \(\Q(i, \sqrt{10})\) None 416.2.k.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
832.2.k.f 832.k 52.f $4$ $6.644$ \(\Q(i, \sqrt{10})\) None 416.2.k.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(1+\cdots)q^{11}+\cdots\)
832.2.k.g 832.k 52.f $8$ $6.644$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 416.2.k.e \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{2}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
832.2.k.h 832.k 52.f $8$ $6.644$ 8.0.18939904.2 None 52.2.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots\)
832.2.k.i 832.k 52.f $8$ $6.644$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 416.2.k.e \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots\)
832.2.k.j 832.k 52.f $12$ $6.644$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 208.2.k.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}-\beta _{5}q^{5}+\beta _{10}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)