Properties

Label 2736.3.o
Level $2736$
Weight $3$
Character orbit 2736.o
Rep. character $\chi_{2736}(721,\cdot)$
Character field $\Q$
Dimension $99$
Newform subspaces $18$
Sturm bound $1440$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1440\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 984 101 883
Cusp forms 936 99 837
Eisenstein series 48 2 46

Trace form

\( 99q + 2q^{5} + 18q^{7} + O(q^{10}) \) \( 99q + 2q^{5} + 18q^{7} - 2q^{11} + 26q^{17} - 31q^{19} + 22q^{23} + 473q^{25} - 148q^{35} - 62q^{43} - 98q^{47} + 713q^{49} + 76q^{55} - 18q^{61} - 106q^{73} + 20q^{77} + 78q^{83} + 140q^{85} - 274q^{95} + O(q^{100}) \)

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.o.a \(1\) \(74.551\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(9\) \(5\) \(q+9q^{5}+5q^{7}+3q^{11}-15q^{17}+19q^{19}+\cdots\)
2736.3.o.b \(2\) \(74.551\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-14\) \(-22\) \(q-7q^{5}-11q^{7}+3q^{11}+2\beta q^{13}+\cdots\)
2736.3.o.c \(2\) \(74.551\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) \(q+(-4-\beta )q^{5}+(-4+3\beta )q^{7}+(-4+\cdots)q^{11}+\cdots\)
2736.3.o.d \(2\) \(74.551\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(-8\) \(10\) \(q-4q^{5}+5q^{7}-10q^{11}-\beta q^{13}-15q^{17}+\cdots\)
2736.3.o.e \(2\) \(74.551\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-8\) \(20\) \(q-4q^{5}+10q^{7}+10q^{11}-7\zeta_{6}q^{13}+\cdots\)
2736.3.o.f \(2\) \(74.551\) \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(-10\) \(q+\beta q^{5}-5q^{7}+5\beta q^{11}+7\beta q^{17}+\cdots\)
2736.3.o.g \(2\) \(74.551\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+2q^{7}-\zeta_{6}q^{13}+(13-\zeta_{6})q^{19}-5^{2}q^{25}+\cdots\)
2736.3.o.h \(2\) \(74.551\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(-10\) \(q+q^{5}-5q^{7}+5q^{11}-2\beta q^{13}+5^{2}q^{17}+\cdots\)
2736.3.o.i \(2\) \(74.551\) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(8\) \(2\) \(q+4q^{5}+q^{7}+14q^{11}+\beta q^{13}-23q^{17}+\cdots\)
2736.3.o.j \(4\) \(74.551\) \(\Q(\sqrt{-7}, \sqrt{10})\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{5}+2q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
2736.3.o.k \(4\) \(74.551\) \(\Q(\sqrt{3}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(10\) \(q+\beta _{1}q^{5}+(3+\beta _{3})q^{7}+\beta _{2}q^{11}+(2\beta _{1}+\cdots)q^{17}+\cdots\)
2736.3.o.l \(4\) \(74.551\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(10\) \(-34\) \(q+(3+\beta _{1})q^{5}+(-9-\beta _{1})q^{7}+(-3+\cdots)q^{11}+\cdots\)
2736.3.o.m \(6\) \(74.551\) 6.0.219615408.1 None \(0\) \(0\) \(2\) \(2\) \(q+\beta _{3}q^{5}+\beta _{2}q^{7}+(-4-\beta _{2})q^{11}+\cdots\)
2736.3.o.n \(8\) \(74.551\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(-4\) \(12\) \(q+(-1-\beta _{1}-\beta _{3})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
2736.3.o.o \(8\) \(74.551\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(-12\) \(q-\beta _{1}q^{5}+(-1-\beta _{7})q^{7}+(-\beta _{1}-\beta _{5}+\cdots)q^{11}+\cdots\)
2736.3.o.p \(8\) \(74.551\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(6\) \(q+(2+\beta _{4})q^{5}+(1-\beta _{3})q^{7}+(-4-\beta _{4}+\cdots)q^{11}+\cdots\)
2736.3.o.q \(20\) \(74.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{10}q^{5}+(1-\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots\)
2736.3.o.r \(20\) \(74.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(q-\beta _{4}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)