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Properties

Label 30.3.d
Level $30$
Weight $3$
Character orbit 30.d
Rep. character $\chi_{30}(11,\cdot)$
Character field $\Q$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q + 4q^{3} - 8q^{4} - 4q^{6} + 8q^{7} - 8q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 8q^{4} - 4q^{6} + 8q^{7} - 8q^{9} - 8q^{12} - 40q^{13} + 20q^{15} + 16q^{16} + 32q^{18} + 32q^{19} - 52q^{21} + 48q^{22} + 8q^{24} - 20q^{25} + 28q^{27} - 16q^{28} - 20q^{30} + 32q^{31} + 24q^{33} - 96q^{34} + 16q^{36} - 88q^{37} - 40q^{39} - 128q^{42} + 56q^{43} + 20q^{45} - 24q^{46} + 16q^{48} + 180q^{49} + 72q^{51} + 80q^{52} + 140q^{54} + 152q^{57} - 40q^{60} - 64q^{61} - 256q^{63} - 32q^{64} + 48q^{66} - 328q^{67} - 132q^{69} + 120q^{70} - 64q^{72} + 200q^{73} - 20q^{75} - 64q^{76} + 40q^{78} - 112q^{79} + 28q^{81} + 192q^{82} + 104q^{84} - 120q^{85} + 240q^{87} - 96q^{88} - 80q^{90} - 80q^{91} + 32q^{93} - 120q^{94} - 16q^{96} + 296q^{97} - 192q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.d.a \(4\) \(0.817\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(4\) \(0\) \(8\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots\)

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

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