Properties

Label 390.2.b
Level $390$
Weight $2$
Character orbit 390.b
Rep. character $\chi_{390}(181,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $168$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(168\)
Trace bound: \(13\)
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 92 12 80
Cusp forms 76 12 64
Eisenstein series 16 0 16

Trace form

\( 12q - 4q^{3} - 12q^{4} + 12q^{9} + O(q^{10}) \) \( 12q - 4q^{3} - 12q^{4} + 12q^{9} + 4q^{10} + 4q^{12} + 4q^{13} + 12q^{16} + 8q^{17} - 12q^{25} + 4q^{26} - 4q^{27} + 8q^{29} + 4q^{30} + 8q^{35} - 12q^{36} - 24q^{38} + 8q^{39} - 4q^{40} - 8q^{42} + 16q^{43} - 4q^{48} - 44q^{49} + 8q^{51} - 4q^{52} - 8q^{53} + 24q^{61} - 8q^{62} - 12q^{64} - 4q^{65} + 8q^{66} - 8q^{68} - 8q^{69} + 8q^{74} + 4q^{75} - 64q^{77} + 8q^{78} + 12q^{81} + 8q^{82} + 8q^{87} + 4q^{90} + 40q^{91} + 16q^{94} + 32q^{95} + O(q^{100}) \)

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.b.a \(2\) \(3.114\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots\)
390.2.b.b \(2\) \(3.114\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots\)
390.2.b.c \(4\) \(3.114\) \(\Q(i, \sqrt{13})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
390.2.b.d \(4\) \(3.114\) \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

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

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