Properties

Label 2736.3.m
Level $2736$
Weight $3$
Character orbit 2736.m
Rep. character $\chi_{2736}(1711,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $7$
Sturm bound $1440$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(1440\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 984 90 894
Cusp forms 936 90 846
Eisenstein series 48 0 48

Trace form

\( 90q + 12q^{5} + O(q^{10}) \) \( 90q + 12q^{5} - 36q^{13} - 12q^{17} + 534q^{25} + 204q^{29} + 12q^{37} - 60q^{41} - 390q^{49} + 60q^{53} + 60q^{61} + 72q^{65} - 300q^{73} + 312q^{77} - 48q^{85} - 204q^{89} - 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2736.3.m.a \(6\) \(74.551\) 6.0.210056875.1 None \(0\) \(0\) \(-14\) \(0\) \(q+(-2+\beta _{2})q^{5}+(\beta _{1}+2\beta _{4}-\beta _{5})q^{7}+\cdots\)
2736.3.m.b \(12\) \(74.551\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{8}q^{7}-\beta _{6}q^{11}+\beta _{1}q^{13}+\cdots\)
2736.3.m.c \(12\) \(74.551\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-\beta _{6}+\beta _{9}+\cdots)q^{11}+\cdots\)
2736.3.m.d \(12\) \(74.551\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{2}q^{5}-\beta _{7}q^{7}+(-\beta _{6}-\beta _{7}-2\beta _{8}+\cdots)q^{11}+\cdots\)
2736.3.m.e \(12\) \(74.551\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(10\) \(0\) \(q+(1+\beta _{1})q^{5}-\beta _{10}q^{7}+(\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{11}+\cdots\)
2736.3.m.f \(12\) \(74.551\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(10\) \(0\) \(q+(1-\beta _{2})q^{5}-\beta _{11}q^{7}+(-\beta _{7}+\beta _{9}+\cdots)q^{11}+\cdots\)
2736.3.m.g \(24\) \(74.551\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)