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Properties

Label 930.2.s
Level $930$
Weight $2$
Character orbit 930.s
Rep. character $\chi_{930}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $4$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 400 64 336
Cusp forms 368 64 304
Eisenstein series 32 0 32

Trace form

\( 64 q - 64 q^{4} - 4 q^{6} + 32 q^{9} + O(q^{10}) \) \( 64 q - 64 q^{4} - 4 q^{6} + 32 q^{9} + 4 q^{10} - 8 q^{15} + 64 q^{16} + 8 q^{19} - 16 q^{21} + 4 q^{24} - 24 q^{25} + 64 q^{29} + 8 q^{30} + 4 q^{31} + 20 q^{34} + 40 q^{35} - 32 q^{36} + 48 q^{39} - 4 q^{40} + 16 q^{41} + 24 q^{46} + 20 q^{49} - 8 q^{54} + 16 q^{55} - 8 q^{59} + 8 q^{60} + 64 q^{61} - 64 q^{64} - 8 q^{65} + 8 q^{66} - 56 q^{70} - 56 q^{71} - 16 q^{75} - 8 q^{76} - 36 q^{79} - 32 q^{81} + 16 q^{84} + 88 q^{85} + 16 q^{86} + 32 q^{89} - 4 q^{90} - 32 q^{91} - 24 q^{94} - 72 q^{95} - 4 q^{96} + O(q^{100}) \)

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.s.a 930.s 155.j $4$ $7.426$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots\)
930.2.s.b 930.s 155.j $8$ $7.426$ 8.0.49787136.1 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{2}q^{3}-q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots\)
930.2.s.c 930.s 155.j $24$ $7.426$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
930.2.s.d 930.s 155.j $28$ $7.426$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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