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Properties

Label 330.2.d
Level $330$
Weight $2$
Character orbit 330.d
Rep. character $\chi_{330}(131,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 64 16 48
Eisenstein series 16 0 16

Trace form

\( 16 q + 4 q^{3} + 16 q^{4} + 4 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{3} + 16 q^{4} + 4 q^{9} + 4 q^{12} + 8 q^{15} + 16 q^{16} + 12 q^{22} - 16 q^{25} - 44 q^{27} - 8 q^{31} + 16 q^{33} + 8 q^{34} + 4 q^{36} - 24 q^{37} - 16 q^{42} + 4 q^{48} - 8 q^{49} - 12 q^{55} - 8 q^{58} + 8 q^{60} + 16 q^{64} - 20 q^{66} - 24 q^{67} + 16 q^{69} - 4 q^{75} - 16 q^{78} + 4 q^{81} - 32 q^{82} + 12 q^{88} - 96 q^{91} + 16 q^{93} - 16 q^{97} - 16 q^{99} + O(q^{100}) \)

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.d.a 330.d 33.d $8$ $2.635$ 8.0.2051727616.3 None \(-8\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(\beta _{3}+\beta _{4})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)
330.2.d.b 330.d 33.d $8$ $2.635$ 8.0.2051727616.3 None \(8\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{3}+\beta _{4})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)

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

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