Properties

Label 930.2.v
Level $930$
Weight $2$
Character orbit 930.v
Rep. character $\chi_{930}(401,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
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.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{10})\)
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 800 160 640
Cusp forms 736 160 576
Eisenstein series 64 0 64

Trace form

\( 160q + 40q^{4} + 24q^{7} + O(q^{10}) \) \( 160q + 40q^{4} + 24q^{7} - 40q^{16} - 16q^{18} - 24q^{19} - 160q^{25} + 60q^{27} + 36q^{28} + 24q^{31} + 52q^{33} + 20q^{34} + 8q^{39} + 100q^{43} - 8q^{45} - 20q^{46} - 64q^{51} - 20q^{55} + 40q^{58} + 72q^{63} + 40q^{64} + 56q^{66} - 72q^{67} + 4q^{69} + 16q^{72} - 40q^{73} - 36q^{76} + 56q^{78} - 80q^{79} + 64q^{81} - 24q^{82} - 40q^{84} - 208q^{87} - 24q^{90} - 100q^{91} + 84q^{93} - 40q^{94} - 156q^{97} + O(q^{100}) \)

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.v.a \(80\) \(7.426\) None \(0\) \(0\) \(0\) \(12\)
930.2.v.b \(80\) \(7.426\) None \(0\) \(0\) \(0\) \(12\)

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

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