Properties

Label 390.2.y
Level $390$
Weight $2$
Character orbit 390.y
Rep. character $\chi_{390}(139,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $7$
Sturm bound $168$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(168\)
Trace bound: \(7\)
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 32 152
Cusp forms 152 32 120
Eisenstein series 32 0 32

Trace form

\( 32q + 16q^{4} + 16q^{9} + O(q^{10}) \) \( 32q + 16q^{4} + 16q^{9} - 4q^{11} - 8q^{14} + 4q^{15} - 16q^{16} + 28q^{19} + 16q^{21} + 8q^{25} + 24q^{29} - 24q^{31} - 20q^{35} - 16q^{36} - 12q^{39} + 24q^{41} - 8q^{44} + 4q^{46} + 36q^{49} + 8q^{50} - 12q^{55} - 4q^{56} - 48q^{59} + 8q^{60} - 16q^{61} - 32q^{64} - 4q^{65} + 40q^{66} - 48q^{70} - 72q^{71} - 4q^{74} - 8q^{75} - 28q^{76} - 56q^{79} - 16q^{81} + 8q^{84} + 4q^{85} - 48q^{86} + 12q^{89} + 12q^{91} + 24q^{94} - 24q^{95} - 8q^{99} + O(q^{100}) \)

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.y.a \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
390.2.y.b \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(-6\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
390.2.y.c \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(6\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots\)
390.2.y.d \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
390.2.y.e \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
390.2.y.f \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
390.2.y.g \(8\) \(3.114\) 8.0.303595776.1 None \(0\) \(0\) \(-12\) \(0\) \(q-\beta _{5}q^{2}-\beta _{5}q^{3}+(1+\beta _{4})q^{4}+(-2+\cdots)q^{5}+\cdots\)

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

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