Properties

Label 756.2.b
Level $756$
Weight $2$
Character orbit 756.b
Rep. character $\chi_{756}(55,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $6$
Sturm bound $288$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\), \(19\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 156 64 92
Cusp forms 132 64 68
Eisenstein series 24 0 24

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{16} + 4 q^{22} - 56 q^{25} - 2 q^{28} + 8 q^{37} + 36 q^{46} - 8 q^{49} + 44 q^{58} + 24 q^{64} - 78 q^{70} + 8 q^{85} - 28 q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
756.2.b.a $4$ $6.037$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots\)
756.2.b.b $4$ $6.037$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
756.2.b.c $12$ $6.037$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{7}q^{2}+(1+\beta _{11})q^{4}-\beta _{8}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.d $12$ $6.037$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.e $16$ $6.037$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{11}q^{5}+\beta _{6}q^{7}+\cdots\)
756.2.b.f $16$ $6.037$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{2}+\beta _{8}q^{4}+\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)