Properties

Label 930.2.br
Level $930$
Weight $2$
Character orbit 930.br
Rep. character $\chi_{930}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $352$
Newform subspaces $2$
Sturm bound $384$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(9\)
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 352 1248
Cusp forms 1472 352 1120
Eisenstein series 128 0 128

Trace form

\( 352q + 88q^{4} + 8q^{7} + O(q^{10}) \) \( 352q + 88q^{4} + 8q^{7} - 88q^{16} + 16q^{18} + 16q^{19} - 60q^{21} + 176q^{25} - 60q^{27} + 72q^{28} + 56q^{31} - 52q^{33} + 28q^{34} + 16q^{39} - 24q^{42} - 80q^{43} + 8q^{45} + 20q^{46} + 60q^{49} + 64q^{51} + 8q^{55} + 192q^{57} - 40q^{58} + 48q^{63} + 88q^{64} - 8q^{66} - 56q^{67} + 164q^{69} - 16q^{72} - 80q^{73} + 24q^{76} - 32q^{78} - 48q^{79} - 232q^{81} - 72q^{82} - 20q^{84} - 8q^{87} + 48q^{90} - 160q^{91} - 132q^{93} - 56q^{94} - 24q^{97} - 192q^{99} + O(q^{100}) \)

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.br.a \(176\) \(7.426\) None \(0\) \(0\) \(0\) \(4\)
930.2.br.b \(176\) \(7.426\) None \(0\) \(0\) \(0\) \(4\)

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

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