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Properties

Label 330.2.u
Level $330$
Weight $2$
Character orbit 330.u
Rep. character $\chi_{330}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $96$
Newform subspaces $2$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.u (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 640 96 544
Cusp forms 512 96 416
Eisenstein series 128 0 128

Trace form

\( 96 q + 16 q^{5} + 40 q^{7} + O(q^{10}) \) \( 96 q + 16 q^{5} + 40 q^{7} - 8 q^{11} + 12 q^{15} + 24 q^{16} + 40 q^{17} + 4 q^{22} - 16 q^{23} + 40 q^{25} - 16 q^{26} + 20 q^{28} - 16 q^{31} + 12 q^{33} + 24 q^{36} - 32 q^{37} + 40 q^{41} - 12 q^{42} - 40 q^{46} - 88 q^{47} - 80 q^{50} - 80 q^{51} - 40 q^{52} - 72 q^{53} - 116 q^{55} + 16 q^{56} - 80 q^{57} - 12 q^{58} - 24 q^{60} - 80 q^{61} - 80 q^{62} - 40 q^{63} - 32 q^{66} + 80 q^{67} - 40 q^{68} + 92 q^{70} + 20 q^{73} - 16 q^{75} + 24 q^{80} + 24 q^{81} - 16 q^{82} + 160 q^{85} - 32 q^{86} + 4 q^{88} - 40 q^{91} + 16 q^{92} + 24 q^{93} - 40 q^{95} - 96 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
330.2.u.a 330.u 55.l $48$ $2.635$ None \(0\) \(0\) \(8\) \(16\) $\mathrm{SU}(2)[C_{20}]$
330.2.u.b 330.u 55.l $48$ $2.635$ None \(0\) \(0\) \(8\) \(24\) $\mathrm{SU}(2)[C_{20}]$

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

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