Properties

Label 2736.2.k
Level $2736$
Weight $2$
Character orbit 2736.k
Rep. character $\chi_{2736}(2431,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $16$
Sturm bound $960$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(960\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(31\)

Dimensions

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

Total New Old
Modular forms 504 50 454
Cusp forms 456 50 406
Eisenstein series 48 0 48

Trace form

\( 50q + O(q^{10}) \) \( 50q - 12q^{17} + 50q^{25} - 82q^{49} - 16q^{61} - 28q^{73} + 12q^{77} - 60q^{85} + O(q^{100}) \)

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.k.a \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(0\) \(q-3q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2736.2.k.b \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(0\) \(q-3q^{5}-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2736.2.k.c \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{6}q^{7}-4\zeta_{6}q^{13}+(-4-\zeta_{6})q^{19}+\cdots\)
2736.2.k.d \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{7}-4\zeta_{6}q^{13}+(4+\zeta_{6})q^{19}+\cdots\)
2736.2.k.e \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{7}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+6q^{17}+\cdots\)
2736.2.k.f \(2\) \(21.847\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{7}+2\zeta_{6}q^{11}+2\zeta_{6}q^{13}+6q^{17}+\cdots\)
2736.2.k.g \(2\) \(21.847\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+\beta q^{7}-\beta q^{11}-7q^{17}-\beta q^{19}+\cdots\)
2736.2.k.h \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2q^{5}-2\beta q^{7}-\beta q^{11}+2\beta q^{13}+\cdots\)
2736.2.k.i \(2\) \(21.847\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2q^{5}-2\beta q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.k.j \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.k.k \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-2\beta _{2}q^{11}-\beta _{3}q^{13}-3q^{17}+\cdots\)
2736.2.k.l \(4\) \(21.847\) \(\Q(\sqrt{-6}, \sqrt{19})\) \(\Q(\sqrt{-57}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{11}+\beta _{2}q^{19}+3\beta _{1}q^{23}-5q^{25}+\cdots\)
2736.2.k.m \(4\) \(21.847\) \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{3}q^{7}+5\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots\)
2736.2.k.n \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
2736.2.k.o \(4\) \(21.847\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{3}q^{5}-\beta _{1}q^{7}+\beta _{1}q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
2736.2.k.p \(8\) \(21.847\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{5}+(\beta _{2}-\beta _{3})q^{7}+(-\beta _{6}+\beta _{7})q^{11}+\cdots\)

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

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