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Properties

Label 858.2.i
Level $858$
Weight $2$
Character orbit 858.i
Rep. character $\chi_{858}(133,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $14$
Sturm bound $336$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 858.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(336\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(858, [\chi])\).

Total New Old
Modular forms 352 48 304
Cusp forms 320 48 272
Eisenstein series 32 0 32

Trace form

\( 48 q - 4 q^{2} - 24 q^{4} - 8 q^{5} + 8 q^{8} - 24 q^{9} + O(q^{10}) \) \( 48 q - 4 q^{2} - 24 q^{4} - 8 q^{5} + 8 q^{8} - 24 q^{9} + 4 q^{10} - 4 q^{13} - 24 q^{16} + 4 q^{17} + 8 q^{18} + 8 q^{19} + 4 q^{20} - 16 q^{21} - 4 q^{22} - 12 q^{23} + 72 q^{25} - 16 q^{26} - 4 q^{29} + 48 q^{31} - 4 q^{32} - 24 q^{34} - 16 q^{35} - 24 q^{36} + 12 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} + 12 q^{41} - 8 q^{42} + 4 q^{45} + 8 q^{46} - 8 q^{47} - 24 q^{49} - 16 q^{51} + 8 q^{52} - 8 q^{53} - 16 q^{57} + 8 q^{58} - 32 q^{59} + 12 q^{61} + 48 q^{64} + 68 q^{65} + 16 q^{66} - 24 q^{67} + 4 q^{68} - 16 q^{69} - 48 q^{70} + 20 q^{71} - 4 q^{72} + 56 q^{73} + 28 q^{74} + 8 q^{75} + 8 q^{76} + 32 q^{79} + 4 q^{80} - 24 q^{81} - 12 q^{82} - 32 q^{83} + 8 q^{84} - 68 q^{85} + 56 q^{86} + 16 q^{87} - 4 q^{88} + 28 q^{89} - 8 q^{90} + 16 q^{91} + 24 q^{92} - 16 q^{93} + 8 q^{94} + 20 q^{97} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(858, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
858.2.i.a 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.a \(-1\) \(-1\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.b 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.b \(-1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.c 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.c \(-1\) \(1\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.d 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.d \(1\) \(-1\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.e 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.e \(1\) \(-1\) \(6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.f 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.f \(1\) \(1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.g 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.g \(1\) \(1\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.h 858.i 13.c $2$ $6.851$ \(\Q(\sqrt{-3}) \) None 858.2.i.h \(1\) \(1\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
858.2.i.i 858.i 13.c $4$ $6.851$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 858.2.i.i \(-2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
858.2.i.j 858.i 13.c $4$ $6.851$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 858.2.i.j \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-1-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
858.2.i.k 858.i 13.c $4$ $6.851$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 858.2.i.k \(2\) \(2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
858.2.i.l 858.i 13.c $6$ $6.851$ 6.0.339692643.1 None 858.2.i.l \(-3\) \(3\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
858.2.i.m 858.i 13.c $6$ $6.851$ 6.0.27870912.1 None 858.2.i.m \(3\) \(-3\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}-\beta _{4}q^{3}+(-1+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
858.2.i.n 858.i 13.c $8$ $6.851$ 8.0.\(\cdots\).1 None 858.2.i.n \(-4\) \(-4\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+\beta _{3}q^{3}+(-1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(858, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(858, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)