Properties

Label 930.2.i
Level $930$
Weight $2$
Character orbit 930.i
Rep. character $\chi_{930}(211,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $14$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

Total New Old
Modular forms 400 40 360
Cusp forms 368 40 328
Eisenstein series 32 0 32

Trace form

\( 40 q + 40 q^{4} - 20 q^{9} + O(q^{10}) \) \( 40 q + 40 q^{4} - 20 q^{9} + 8 q^{11} - 24 q^{13} + 8 q^{14} + 40 q^{16} - 8 q^{17} + 64 q^{23} - 20 q^{25} + 8 q^{26} + 16 q^{29} + 8 q^{30} + 32 q^{33} + 4 q^{34} + 32 q^{35} - 20 q^{36} + 8 q^{37} + 24 q^{38} - 8 q^{42} - 32 q^{43} + 8 q^{44} + 8 q^{46} + 16 q^{47} - 20 q^{49} + 16 q^{51} - 24 q^{52} + 24 q^{53} + 4 q^{55} + 8 q^{56} - 24 q^{57} + 16 q^{58} + 40 q^{64} - 24 q^{66} - 16 q^{67} - 8 q^{68} + 16 q^{71} - 16 q^{73} - 24 q^{74} - 16 q^{77} - 16 q^{78} + 20 q^{79} - 20 q^{81} + 24 q^{82} - 8 q^{83} + 8 q^{87} + 32 q^{89} + 48 q^{91} + 64 q^{92} - 8 q^{93} + 56 q^{94} + 48 q^{97} - 32 q^{98} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
930.2.i.a 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots\)
930.2.i.b 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.c 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.d 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.e 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.f 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.g 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.h 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.i 930.i 31.c $2$ $7.426$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.j 930.i 31.c $4$ $7.426$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-4\) \(-2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
930.2.i.k 930.i 31.c $4$ $7.426$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.l 930.i 31.c $4$ $7.426$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(4\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.m 930.i 31.c $4$ $7.426$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.n 930.i 31.c $6$ $7.426$ 6.0.3636603.4 None \(-6\) \(3\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)