Properties

Label 390.2.x
Level $390$
Weight $2$
Character orbit 390.x
Rep. character $\chi_{390}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $168$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(390, [\chi])\).

Total New Old
Modular forms 184 24 160
Cusp forms 152 24 128
Eisenstein series 32 0 32

Trace form

\( 24 q - 12 q^{4} + 12 q^{9} + O(q^{10}) \) \( 24 q - 12 q^{4} + 12 q^{9} + 2 q^{10} + 12 q^{11} + 8 q^{14} + 12 q^{15} - 12 q^{16} - 12 q^{19} + 6 q^{20} - 20 q^{25} - 4 q^{26} + 28 q^{29} + 4 q^{35} + 12 q^{36} - 4 q^{39} - 4 q^{40} - 36 q^{41} - 6 q^{45} - 12 q^{46} + 16 q^{49} - 30 q^{50} + 32 q^{51} - 20 q^{55} - 4 q^{56} - 72 q^{59} + 20 q^{61} + 24 q^{64} - 38 q^{65} - 24 q^{66} + 32 q^{69} - 24 q^{71} - 24 q^{74} + 8 q^{75} + 12 q^{76} + 8 q^{79} - 6 q^{80} - 12 q^{81} + 24 q^{84} + 66 q^{85} + 36 q^{89} + 4 q^{90} + 4 q^{91} - 16 q^{94} - 24 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(390, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
390.2.x.a $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(-2\) \(-2\) \(q+(-1-\beta _{6})q^{2}+\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
390.2.x.b $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(2\) \(2\) \(q+(1+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(390, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)