Properties

Label 390.2.bb
Level $390$
Weight $2$
Character orbit 390.bb
Rep. character $\chi_{390}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $3$
Sturm bound $168$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(10\)
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 16 168
Cusp forms 152 16 136
Eisenstein series 32 0 32

Trace form

\( 16q + 8q^{4} - 8q^{9} + O(q^{10}) \) \( 16q + 8q^{4} - 8q^{9} - 4q^{10} + 12q^{11} - 8q^{13} + 24q^{14} - 8q^{16} + 16q^{17} + 12q^{19} - 16q^{25} - 16q^{26} - 8q^{29} - 4q^{30} + 4q^{35} + 8q^{36} + 24q^{37} - 4q^{39} - 8q^{40} + 8q^{42} - 8q^{43} - 12q^{46} + 12q^{49} - 32q^{51} + 8q^{52} - 16q^{53} - 12q^{55} + 12q^{56} - 24q^{58} + 24q^{59} - 8q^{61} + 8q^{62} - 16q^{64} - 20q^{65} - 8q^{66} + 24q^{67} - 16q^{68} + 8q^{69} - 72q^{71} + 4q^{74} + 12q^{76} + 16q^{77} + 16q^{78} - 8q^{79} - 8q^{81} - 8q^{82} - 8q^{87} + 12q^{89} + 8q^{90} + 20q^{91} + 48q^{93} - 16q^{94} + 16q^{95} + 48q^{98} + O(q^{100}) \)

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.bb.a \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
390.2.bb.b \(4\) \(3.114\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
390.2.bb.c \(8\) \(3.114\) 8.0.\(\cdots\).1 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{6}q^{3}+(1-\beta _{6})q^{4}-\beta _{2}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)