Properties

Label 2736.2.dc
Level $2736$
Weight $2$
Character orbit 2736.dc
Rep. character $\chi_{2736}(449,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $6$
Sturm bound $960$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.dc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(960\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 1008 80 928
Cusp forms 912 80 832
Eisenstein series 96 0 96

Trace form

\( 80q + 8q^{7} + O(q^{10}) \) \( 80q + 8q^{7} - 16q^{19} + 40q^{25} + 4q^{43} + 64q^{49} - 24q^{55} - 32q^{61} - 60q^{67} + 8q^{73} - 84q^{79} - 12q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2736.2.dc.a \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{5}+(1-2\beta _{1}+\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2736.2.dc.b \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{5}+(1+2\beta _{1}-\beta _{3})q^{7}+(2-4\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.dc.c \(16\) \(21.847\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{10}q^{5}-\beta _{14}q^{7}-\beta _{7}q^{11}+(-2+\cdots)q^{13}+\cdots\)
2736.2.dc.d \(16\) \(21.847\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{10})q^{5}+(-\beta _{7}-\beta _{8})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.dc.e \(20\) \(21.847\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(\beta _{6}+\beta _{18}+\cdots)q^{11}+\cdots\)
2736.2.dc.f \(20\) \(21.847\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)