Properties

Label 30.3.f
Level $30$
Weight $3$
Character orbit 30.f
Rep. character $\chi_{30}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 30.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(30, [\chi])\).

Total New Old
Modular forms 32 4 28
Cusp forms 16 4 12
Eisenstein series 16 0 16

Trace form

\( 4q + 4q^{2} - 16q^{7} - 8q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 16q^{7} - 8q^{8} + 4q^{10} - 16q^{11} + 12q^{13} - 24q^{15} - 16q^{16} + 44q^{17} + 12q^{18} + 8q^{20} + 48q^{21} - 16q^{22} - 16q^{23} + 92q^{25} + 24q^{26} + 32q^{28} - 48q^{30} - 80q^{31} - 16q^{32} - 48q^{33} - 112q^{35} + 24q^{36} - 108q^{37} - 64q^{38} + 8q^{40} + 32q^{41} + 48q^{42} + 48q^{43} - 12q^{45} - 32q^{46} + 96q^{47} + 92q^{50} + 48q^{51} + 24q^{52} + 100q^{53} + 192q^{55} + 64q^{56} + 48q^{57} + 64q^{58} - 48q^{60} - 96q^{61} - 80q^{62} - 48q^{63} - 204q^{65} - 96q^{66} - 16q^{67} - 88q^{68} - 32q^{70} + 64q^{71} + 24q^{72} - 188q^{73} + 48q^{75} - 128q^{76} - 128q^{77} + 96q^{78} - 36q^{81} + 32q^{82} + 192q^{83} - 52q^{85} + 96q^{86} - 48q^{87} + 32q^{88} - 12q^{90} + 288q^{91} - 32q^{92} - 96q^{93} + 64q^{95} + 132q^{97} - 124q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.3.f.a \(4\) \(0.817\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(-16\) \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)