Properties

Label 390.2.i
Level $390$
Weight $2$
Character orbit 390.i
Rep. character $\chi_{390}(61,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(168\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 184 16 168
Cusp forms 152 16 136
Eisenstein series 32 0 32

Trace form

\( 16q - 8q^{4} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{4} - 8q^{9} - 4q^{10} + 12q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 4q^{19} - 16q^{22} + 16q^{23} + 16q^{25} - 8q^{29} - 4q^{30} + 8q^{31} + 16q^{34} + 4q^{35} - 8q^{36} + 8q^{37} - 12q^{39} + 8q^{40} - 24q^{41} - 8q^{42} + 8q^{43} - 24q^{44} + 4q^{46} + 16q^{47} - 12q^{49} - 8q^{52} + 48q^{53} - 4q^{55} - 4q^{56} - 16q^{57} - 8q^{58} - 16q^{59} - 8q^{61} - 8q^{62} + 16q^{64} + 12q^{65} - 8q^{66} - 24q^{67} - 8q^{69} + 40q^{71} - 48q^{73} + 4q^{74} + 4q^{76} - 16q^{77} + 16q^{78} + 24q^{79} - 8q^{81} - 24q^{82} + 48q^{83} + 48q^{86} - 8q^{87} - 16q^{88} + 36q^{89} + 8q^{90} - 4q^{91} - 32q^{92} - 8q^{94} + 16q^{95} - 16q^{97} + 16q^{98} - 24q^{99} + O(q^{100}) \)

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.i.a \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-2\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.b \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(2\) \(3\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.c \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-2\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.d \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-2\) \(5\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.e \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-2\) \(-3\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.f \(2\) \(3.114\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(2\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.g \(4\) \(3.114\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(4\) \(-3\) \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)