Properties

Label 2736.2.f
Level $2736$
Weight $2$
Character orbit 2736.f
Rep. character $\chi_{2736}(1025,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $9$
Sturm bound $960$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(960\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(29\)

Dimensions

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

Total New Old
Modular forms 504 40 464
Cusp forms 456 40 416
Eisenstein series 48 0 48

Trace form

\( 40q - 8q^{7} + O(q^{10}) \) \( 40q - 8q^{7} + 4q^{19} - 40q^{25} + 8q^{43} + 56q^{49} - 48q^{55} + 32q^{61} + 16q^{73} + O(q^{100}) \)

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.f.a \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.b \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.c \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.f.d \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots\)
2736.2.f.e \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
2736.2.f.f \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{5}+2q^{7}-\beta _{1}q^{11}+2\beta _{2}q^{13}+\cdots\)
2736.2.f.g \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots\)
2736.2.f.h \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots\)
2736.2.f.i \(8\) \(21.847\) 8.0.\(\cdots\).4 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{6}q^{11}+(\beta _{3}-\beta _{5}+\cdots)q^{17}+\cdots\)

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

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