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Properties

Label 930.2.bn
Level $930$
Weight $2$
Character orbit 930.bn
Rep. character $\chi_{930}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
Newform subspaces $2$
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.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
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 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

Trace form

\( 256 q + 64 q^{4} - 16 q^{6} - 32 q^{9} + O(q^{10}) \) \( 256 q + 64 q^{4} - 16 q^{6} - 32 q^{9} - 4 q^{10} + 8 q^{15} - 64 q^{16} - 8 q^{19} + 56 q^{21} - 4 q^{24} + 24 q^{25} + 16 q^{29} - 8 q^{30} - 4 q^{31} + 20 q^{34} - 40 q^{35} - 128 q^{36} + 32 q^{39} - 6 q^{40} + 24 q^{41} - 4 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{54} - 96 q^{55} + 88 q^{59} - 8 q^{60} + 176 q^{61} + 64 q^{64} - 152 q^{65} + 12 q^{66} + 16 q^{70} + 256 q^{71} - 24 q^{75} + 48 q^{76} - 24 q^{79} + 32 q^{81} - 16 q^{84} + 92 q^{85} - 136 q^{86} + 88 q^{89} + 4 q^{90} - 48 q^{91} + 24 q^{94} + 52 q^{95} + 4 q^{96} + O(q^{100}) \)

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.bn.a 930.bn 155.u $112$ $7.426$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{30}]$
930.2.bn.b 930.bn 155.u $144$ $7.426$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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