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Properties

Label 930.2.o
Level $930$
Weight $2$
Character orbit 930.o
Rep. character $\chi_{930}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $5$
Sturm bound $384$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 400 88 312
Cusp forms 368 88 280
Eisenstein series 32 0 32

Trace form

\( 88 q - 88 q^{4} - 8 q^{7} + O(q^{10}) \) \( 88 q - 88 q^{4} - 8 q^{7} + 88 q^{16} - 16 q^{18} - 16 q^{19} + 60 q^{21} + 44 q^{25} + 8 q^{28} + 24 q^{31} - 8 q^{33} + 12 q^{34} - 16 q^{39} + 24 q^{42} - 8 q^{45} - 60 q^{49} + 16 q^{51} + 12 q^{55} - 12 q^{57} + 112 q^{63} - 88 q^{64} - 32 q^{66} + 56 q^{67} - 4 q^{69} + 16 q^{72} + 120 q^{73} + 16 q^{76} - 48 q^{78} - 12 q^{79} - 48 q^{81} - 8 q^{82} - 60 q^{84} + 8 q^{87} - 8 q^{90} + 32 q^{93} - 24 q^{94} - 96 q^{97} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.o.a 930.o 93.g $4$ $7.426$ \(\Q(\zeta_{12})\) None \(0\) \(-6\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+(-1-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
930.2.o.b 930.o 93.g $4$ $7.426$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
930.2.o.c 930.o 93.g $4$ $7.426$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
930.2.o.d 930.o 93.g $36$ $7.426$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$
930.2.o.e 930.o 93.g $40$ $7.426$ None \(0\) \(6\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$

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

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