Properties

Label 1386.2.a
Level $1386$
Weight $2$
Character orbit 1386.a
Rep. character $\chi_{1386}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $18$
Sturm bound $576$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(576\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1386))\).

Total New Old
Modular forms 304 26 278
Cusp forms 273 26 247
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(19\)

Trace form

\( 26q + 2q^{2} + 26q^{4} + 2q^{8} + O(q^{10}) \) \( 26q + 2q^{2} + 26q^{4} + 2q^{8} + 4q^{10} - 2q^{11} + 4q^{13} - 4q^{14} + 26q^{16} + 12q^{17} + 8q^{19} + 2q^{22} + 8q^{23} + 54q^{25} + 16q^{26} + 28q^{29} + 16q^{31} + 2q^{32} + 12q^{34} + 8q^{35} + 28q^{37} + 12q^{38} + 4q^{40} - 4q^{41} + 8q^{43} - 2q^{44} - 24q^{47} + 26q^{49} + 6q^{50} + 4q^{52} - 4q^{53} + 12q^{55} - 4q^{56} + 4q^{58} - 4q^{59} + 36q^{61} - 8q^{62} + 26q^{64} - 16q^{65} + 12q^{68} + 4q^{70} + 8q^{71} - 28q^{73} + 28q^{74} + 8q^{76} - 4q^{77} - 32q^{79} + 12q^{82} + 16q^{83} + 24q^{85} - 8q^{86} + 2q^{88} + 20q^{89} - 4q^{91} + 8q^{92} - 24q^{94} - 8q^{95} + 44q^{97} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11
1386.2.a.a \(1\) \(11.067\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1386.2.a.b \(1\) \(11.067\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1386.2.a.c \(1\) \(11.067\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
1386.2.a.d \(1\) \(11.067\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
1386.2.a.e \(1\) \(11.067\) \(\Q\) None \(-1\) \(0\) \(4\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots\)
1386.2.a.f \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.g \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.h \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.i \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
1386.2.a.j \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+6q^{13}+\cdots\)
1386.2.a.k \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
1386.2.a.l \(1\) \(11.067\) \(\Q\) None \(1\) \(0\) \(4\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots\)
1386.2.a.m \(2\) \(11.067\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
1386.2.a.n \(2\) \(11.067\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{7}-q^{8}-\beta q^{10}+\cdots\)
1386.2.a.o \(2\) \(11.067\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1386.2.a.p \(2\) \(11.067\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1386.2.a.q \(3\) \(11.067\) 3.3.1304.1 None \(-3\) \(0\) \(-2\) \(3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{7}-q^{8}+\cdots\)
1386.2.a.r \(3\) \(11.067\) 3.3.1304.1 None \(3\) \(0\) \(2\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+(1+\beta _{2})q^{5}+q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1386))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1386)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)