Properties

Label 330.2.w
Level $330$
Weight $2$
Character orbit 330.w
Rep. character $\chi_{330}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $192$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(330, [\chi])\).

Total New Old
Modular forms 640 192 448
Cusp forms 512 192 320
Eisenstein series 128 0 128

Trace form

\( 192q + 4q^{3} + 8q^{7} + O(q^{10}) \) \( 192q + 4q^{3} + 8q^{7} - 8q^{10} + 16q^{12} - 16q^{13} + 4q^{15} + 48q^{16} - 16q^{21} + 4q^{22} + 48q^{25} + 4q^{27} - 12q^{28} - 16q^{31} - 92q^{33} + 16q^{36} - 40q^{37} - 32q^{42} - 128q^{43} + 32q^{45} - 24q^{46} - 4q^{48} + 88q^{51} - 24q^{52} - 68q^{55} - 48q^{57} - 84q^{58} - 4q^{60} - 48q^{61} - 40q^{63} - 8q^{66} - 208q^{67} - 12q^{70} + 76q^{73} + 92q^{75} - 16q^{78} - 96q^{81} - 16q^{82} - 16q^{85} + 64q^{87} + 4q^{88} + 48q^{90} - 240q^{91} + 28q^{93} + 64q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(330, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
330.2.w.a \(192\) \(2.635\) None \(0\) \(4\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)