Properties

Label 2736.2.bm
Level $2736$
Weight $2$
Character orbit 2736.bm
Rep. character $\chi_{2736}(559,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $100$
Newform subspaces $20$
Sturm bound $960$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 20 \)
Sturm bound: \(960\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(23\), \(31\)

Dimensions

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

Total New Old
Modular forms 1008 100 908
Cusp forms 912 100 812
Eisenstein series 96 0 96

Trace form

\( 100q + O(q^{10}) \) \( 100q - 12q^{13} + 12q^{17} - 50q^{25} + 18q^{41} - 68q^{49} - 36q^{53} - 8q^{61} - 14q^{73} - 48q^{77} - 12q^{85} - 72q^{89} + 18q^{97} + O(q^{100}) \)

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.bm.a \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(1-2\zeta_{6})q^{7}+(-2+4\zeta_{6})q^{11}+(-6+\cdots)q^{13}+\cdots\)
2736.2.bm.b \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-1+2\zeta_{6})q^{7}+(2-4\zeta_{6})q^{11}+(-6+\cdots)q^{13}+\cdots\)
2736.2.bm.c \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-3+6\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+\cdots\)
2736.2.bm.d \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(3-6\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
2736.2.bm.e \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-1+2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+(-3+\cdots)q^{19}+\cdots\)
2736.2.bm.f \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(1-2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+(3+2\zeta_{6})q^{19}+\cdots\)
2736.2.bm.g \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(3-3\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+(2-4\zeta_{6})q^{11}+\cdots\)
2736.2.bm.h \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(3-3\zeta_{6})q^{5}+(-2+4\zeta_{6})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2736.2.bm.i \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+2\beta _{2})q^{5}+(1-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
2736.2.bm.j \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+2\beta _{2})q^{5}+(-1+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
2736.2.bm.k \(4\) \(21.847\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\zeta_{12}^{2})q^{5}-2\zeta_{12}^{3}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2736.2.bm.l \(6\) \(21.847\) 6.0.31726512.1 None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\beta _{1}-\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
2736.2.bm.m \(6\) \(21.847\) 6.0.31726512.1 None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\beta _{1}-\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
2736.2.bm.n \(6\) \(21.847\) 6.0.954288.1 None \(0\) \(0\) \(2\) \(0\) \(q+(1-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2736.2.bm.o \(6\) \(21.847\) 6.0.954288.1 None \(0\) \(0\) \(2\) \(0\) \(q+(1-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots\)
2736.2.bm.p \(8\) \(21.847\) 8.0.897122304.10 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
2736.2.bm.q \(8\) \(21.847\) 8.0.897122304.10 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
2736.2.bm.r \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
2736.2.bm.s \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+(1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
2736.2.bm.t \(16\) \(21.847\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{5}+(\beta _{3}+\beta _{5})q^{7}+(\beta _{11}-\beta _{12}+\cdots)q^{11}+\cdots\)

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

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