Properties

Label 1386.2.k
Level $1386$
Weight $2$
Character orbit 1386.k
Rep. character $\chi_{1386}(793,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $23$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 23 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\), \(23\)

Dimensions

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

Total New Old
Modular forms 608 64 544
Cusp forms 544 64 480
Eisenstein series 64 0 64

Trace form

\( 64q - 32q^{4} - 4q^{5} - 8q^{7} + O(q^{10}) \) \( 64q - 32q^{4} - 4q^{5} - 8q^{7} + 8q^{13} + 8q^{14} - 32q^{16} + 12q^{17} + 16q^{19} + 8q^{20} - 16q^{25} - 12q^{26} + 4q^{28} - 8q^{29} - 28q^{31} - 24q^{34} + 28q^{35} - 16q^{37} - 20q^{38} - 40q^{41} + 56q^{43} - 20q^{46} + 8q^{47} + 16q^{49} - 4q^{52} + 4q^{53} - 4q^{56} + 12q^{58} - 20q^{59} - 20q^{61} - 24q^{62} + 64q^{64} + 44q^{65} - 36q^{67} + 12q^{68} - 4q^{70} + 8q^{71} + 48q^{73} + 36q^{74} - 32q^{76} + 4q^{77} + 4q^{79} - 4q^{80} + 8q^{82} - 72q^{83} - 96q^{85} - 4q^{86} - 40q^{89} - 4q^{91} + 40q^{94} + 12q^{95} + 80q^{97} + 48q^{98} + O(q^{100}) \)

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.k.a \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1386.2.k.b \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
1386.2.k.c \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
1386.2.k.d \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1386.2.k.e \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
1386.2.k.f \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
1386.2.k.g \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1386.2.k.h \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.i \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.j \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
1386.2.k.k \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1386.2.k.l \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1386.2.k.m \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1386.2.k.n \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1386.2.k.o \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.p \(2\) \(11.067\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
1386.2.k.q \(4\) \(11.067\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-2\) \(-2\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1386.2.k.r \(4\) \(11.067\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}-\beta _{1}q^{7}+\cdots\)
1386.2.k.s \(4\) \(11.067\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(2\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.t \(4\) \(11.067\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-4\) \(-2\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.u \(4\) \(11.067\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(-2\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.v \(6\) \(11.067\) 6.0.21870000.1 None \(3\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1386.2.k.w \(6\) \(11.067\) 6.0.1156923.1 None \(3\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{4}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)