Properties

Label 330.2.j
Level $330$
Weight $2$
Character orbit 330.j
Rep. character $\chi_{330}(23,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $2$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 160 40 120
Cusp forms 128 40 88
Eisenstein series 32 0 32

Trace form

\( 40q + 4q^{3} + 8q^{6} + O(q^{10}) \) \( 40q + 4q^{3} + 8q^{6} - 4q^{12} + 16q^{13} - 20q^{15} - 40q^{16} - 16q^{18} + 24q^{25} + 4q^{27} + 24q^{30} + 32q^{31} - 4q^{33} - 8q^{36} - 8q^{37} - 16q^{40} + 24q^{42} - 16q^{45} - 48q^{46} - 4q^{48} - 32q^{51} - 16q^{52} - 24q^{55} - 16q^{58} + 12q^{60} + 16q^{61} + 48q^{63} + 40q^{67} - 16q^{70} + 16q^{72} - 16q^{73} + 12q^{75} - 32q^{76} + 16q^{78} + 48q^{82} - 104q^{87} + 16q^{90} - 104q^{93} - 8q^{96} - 88q^{97} + O(q^{100}) \)

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.j.a \(20\) \(2.635\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{3}q^{3}-\beta _{14}q^{4}+(\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
330.2.j.b \(20\) \(2.635\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{1}q^{3}-\beta _{14}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)