Properties

Label 1386.2.e
Level $1386$
Weight $2$
Character orbit 1386.e
Rep. character $\chi_{1386}(307,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $5$
Sturm bound $576$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 304 40 264
Cusp forms 272 40 232
Eisenstein series 32 0 32

Trace form

\( 40q - 40q^{4} + O(q^{10}) \) \( 40q - 40q^{4} + 12q^{11} + 8q^{14} + 40q^{16} - 4q^{22} - 16q^{23} - 32q^{25} - 40q^{37} - 12q^{44} - 24q^{49} + 56q^{53} - 8q^{56} - 24q^{58} - 40q^{64} + 8q^{67} + 24q^{70} - 32q^{71} + 12q^{77} + 32q^{86} + 4q^{88} + 40q^{91} + 16q^{92} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1386.2.e.a \(8\) \(11.067\) 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1386.2.e.b \(8\) \(11.067\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1386.2.e.c \(8\) \(11.067\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-q^{4}-\beta _{5}q^{5}+\beta _{1}q^{7}-\beta _{2}q^{8}+\cdots\)
1386.2.e.d \(8\) \(11.067\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{2}-\beta _{7})q^{7}+\cdots\)
1386.2.e.e \(8\) \(11.067\) 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)