Properties

Label 2736.2.s
Level $2736$
Weight $2$
Character orbit 2736.s
Rep. character $\chi_{2736}(577,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $98$
Newform subspaces $29$
Sturm bound $960$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 29 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 1008 102 906
Cusp forms 912 98 814
Eisenstein series 96 4 92

Trace form

\( 98q + q^{5} + O(q^{10}) \) \( 98q + q^{5} - 4q^{11} - q^{13} + 5q^{17} + 10q^{19} + 5q^{23} - 46q^{25} + q^{29} + 32q^{31} - 12q^{35} - 4q^{37} + 7q^{41} - 3q^{43} + 5q^{47} + 66q^{49} + 5q^{53} + 24q^{55} - 19q^{59} - 13q^{61} + 26q^{65} + 9q^{67} + 7q^{71} + 9q^{73} + 24q^{77} + 13q^{79} - 60q^{83} + 9q^{85} + 13q^{89} - 12q^{91} + 65q^{95} + q^{97} + O(q^{100}) \)

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.s.a \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-4+4\zeta_{6})q^{5}+3q^{11}-2\zeta_{6}q^{13}+\cdots\)
2736.2.s.b \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(6\) \(q+(-4+4\zeta_{6})q^{5}+3q^{7}-4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.c \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(6\) \(q+(-4+4\zeta_{6})q^{5}+3q^{7}+2q^{11}+7\zeta_{6}q^{13}+\cdots\)
2736.2.s.d \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-6\) \(q+(-2+2\zeta_{6})q^{5}-3q^{7}-2q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.e \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-6\) \(q+(-2+2\zeta_{6})q^{5}-3q^{7}+6q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.f \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(10\) \(q+(-2+2\zeta_{6})q^{5}+5q^{7}-4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.g \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{5}-4q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.h \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-10\) \(q-5q^{7}-5\zeta_{6}q^{13}+(-3-2\zeta_{6})q^{19}+\cdots\)
2736.2.s.i \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-6\) \(q-3q^{7}+2q^{11}-\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
2736.2.s.j \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-2q^{11}-5\zeta_{6}q^{13}+(-4+4\zeta_{6})q^{17}+\cdots\)
2736.2.s.k \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-2q^{11}+3\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
2736.2.s.l \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+7\zeta_{6}q^{13}+(-5+2\zeta_{6})q^{19}+\cdots\)
2736.2.s.m \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(8\) \(q+4q^{7}+3q^{11}-2\zeta_{6}q^{13}+(-6+6\zeta_{6})q^{17}+\cdots\)
2736.2.s.n \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-6\) \(q+(2-2\zeta_{6})q^{5}-3q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.o \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-6\) \(q+(2-2\zeta_{6})q^{5}-3q^{7}+2q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.p \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(6\) \(q+(2-2\zeta_{6})q^{5}+3q^{7}-5\zeta_{6}q^{13}+(-4+\cdots)q^{17}+\cdots\)
2736.2.s.q \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(3-3\zeta_{6})q^{5}-4q^{11}+5\zeta_{6}q^{13}+\cdots\)
2736.2.s.r \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(6\) \(q+(4-4\zeta_{6})q^{5}+3q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.s \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(-2\) \(-8\) \(q+(-1-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
2736.2.s.t \(4\) \(21.847\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{2}q^{5}+(1-\beta _{3})q^{7}+\beta _{3}q^{11}+(1+\cdots)q^{13}+\cdots\)
2736.2.s.u \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(2\) \(-8\) \(q+(1+\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
2736.2.s.v \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(2\) \(-4\) \(q+(1+\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
2736.2.s.w \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(3-\beta _{3})q^{11}+\cdots\)
2736.2.s.x \(6\) \(21.847\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+(-1+\zeta_{18}^{5})q^{7}+\cdots\)
2736.2.s.y \(6\) \(21.847\) 6.0.2696112.1 None \(0\) \(0\) \(1\) \(4\) \(q+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.s.z \(6\) \(21.847\) 6.0.954288.1 None \(0\) \(0\) \(2\) \(2\) \(q+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.s.ba \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-4\) \(4\) \(q+(\beta _{3}+\beta _{5})q^{5}+(1-\beta _{6})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.s.bb \(8\) \(21.847\) 8.0.764411904.5 None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{5}+(1+\beta _{5})q^{7}+(\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{11}+\cdots\)
2736.2.s.bc \(8\) \(21.847\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(4\) \(4\) \(q+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(1-\beta _{6})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)