Properties

Label 390.2.e
Level $390$
Weight $2$
Character orbit 390.e
Rep. character $\chi_{390}(79,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(10\)
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

\( 12q - 12q^{4} + 8q^{5} - 4q^{6} - 12q^{9} + O(q^{10}) \) \( 12q - 12q^{4} + 8q^{5} - 4q^{6} - 12q^{9} + 4q^{10} - 16q^{11} + 4q^{15} + 12q^{16} + 8q^{19} - 8q^{20} - 8q^{21} + 4q^{24} + 4q^{25} + 8q^{30} + 8q^{31} + 16q^{34} - 24q^{35} + 12q^{36} - 4q^{40} + 16q^{41} + 16q^{44} - 8q^{45} - 32q^{46} - 12q^{49} + 8q^{51} + 4q^{54} + 16q^{55} + 16q^{59} - 4q^{60} - 40q^{61} - 12q^{64} - 8q^{65} - 8q^{69} - 8q^{70} - 16q^{74} - 8q^{76} + 32q^{79} + 8q^{80} + 12q^{81} + 8q^{84} - 24q^{85} + 32q^{86} + 32q^{89} - 4q^{90} - 16q^{94} + 24q^{95} - 4q^{96} + 16q^{99} + O(q^{100}) \)

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

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

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)