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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.2.s.a \(4\) \(7.426\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots\)
930.2.s.b \(8\) \(7.426\) 8.0.49787136.1 None \(0\) \(0\) \(-8\) \(0\) \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{2}q^{3}-q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots\)
930.2.s.c \(24\) \(7.426\) None \(0\) \(0\) \(4\) \(0\)
930.2.s.d \(28\) \(7.426\) None \(0\) \(0\) \(2\) \(0\)

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

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