Properties

Label 1386.2.c
Level $1386$
Weight $2$
Character orbit 1386.c
Rep. character $\chi_{1386}(197,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $576$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 304 24 280
Cusp forms 272 24 248
Eisenstein series 32 0 32

Trace form

\( 24q + 24q^{4} + O(q^{10}) \) \( 24q + 24q^{4} + 24q^{16} - 8q^{22} - 8q^{25} + 32q^{34} + 48q^{37} - 24q^{49} - 16q^{55} + 32q^{58} + 24q^{64} - 96q^{67} - 16q^{70} + 32q^{82} - 8q^{88} + 96q^{97} + O(q^{100}) \)

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.c.a \(12\) \(11.067\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots\)
1386.2.c.b \(12\) \(11.067\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)