Properties

Label 330.2.m
Level $330$
Weight $2$
Character orbit 330.m
Rep. character $\chi_{330}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $32$
Newform subspaces $6$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 320 32 288
Cusp forms 256 32 224
Eisenstein series 64 0 64

Trace form

\( 32q - 8q^{4} - 8q^{9} + O(q^{10}) \) \( 32q - 8q^{4} - 8q^{9} + 16q^{10} + 28q^{11} + 16q^{13} - 4q^{14} - 8q^{16} + 8q^{17} - 8q^{19} - 8q^{22} + 16q^{23} - 8q^{25} - 16q^{26} + 24q^{29} - 4q^{30} - 8q^{31} - 8q^{33} + 24q^{34} - 8q^{35} - 8q^{36} + 16q^{37} - 24q^{38} - 8q^{39} - 4q^{40} - 4q^{41} - 8q^{42} + 16q^{43} - 12q^{44} + 4q^{46} - 52q^{49} + 8q^{51} - 24q^{52} - 48q^{53} + 8q^{55} - 24q^{56} - 8q^{57} - 32q^{58} - 40q^{59} + 16q^{61} + 24q^{62} - 8q^{64} - 8q^{65} + 8q^{66} + 48q^{67} + 8q^{68} - 24q^{69} - 56q^{71} + 64q^{73} + 40q^{74} - 8q^{76} + 80q^{77} + 52q^{79} - 8q^{81} + 24q^{82} + 8q^{83} - 8q^{85} - 24q^{86} - 16q^{87} + 32q^{88} - 8q^{89} - 4q^{90} - 92q^{91} - 24q^{92} - 48q^{93} + 12q^{94} - 72q^{97} - 32q^{98} - 12q^{99} + O(q^{100}) \)

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.m.a \(4\) \(2.635\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(5\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
330.2.m.b \(4\) \(2.635\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(1\) \(-4\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
330.2.m.c \(4\) \(2.635\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-1\) \(4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
330.2.m.d \(4\) \(2.635\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(1\) \(-5\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
330.2.m.e \(8\) \(2.635\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(-3\) \(q-\beta _{2}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
330.2.m.f \(8\) \(2.635\) 8.0.2769390625.1 None \(2\) \(-2\) \(2\) \(3\) \(q-\beta _{5}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)