Properties

Label 2646.2.e
Level $2646$
Weight $2$
Character orbit 2646.e
Rep. character $\chi_{2646}(1549,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $20$
Sturm bound $1008$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(1008\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

Total New Old
Modular forms 1104 80 1024
Cusp forms 912 80 832
Eisenstein series 192 0 192

Trace form

\( 80q + 80q^{4} - 4q^{5} + O(q^{10}) \) \( 80q + 80q^{4} - 4q^{5} + 8q^{11} - 2q^{13} + 80q^{16} - 14q^{17} + 4q^{19} - 4q^{20} + 2q^{23} - 40q^{25} - 16q^{26} - 18q^{29} + 4q^{31} - 2q^{37} - 12q^{38} - 6q^{41} - 2q^{43} + 8q^{44} + 6q^{46} + 12q^{47} - 2q^{52} + 32q^{53} + 12q^{55} - 6q^{58} + 44q^{59} + 16q^{61} + 44q^{62} + 80q^{64} - 4q^{65} + 28q^{67} - 14q^{68} + 76q^{71} + 28q^{73} - 6q^{74} + 4q^{76} + 64q^{79} - 4q^{80} + 16q^{83} - 24q^{85} + 20q^{86} - 36q^{89} + 2q^{92} + 24q^{94} - 84q^{95} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2646.2.e.a \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}+(-1+\zeta_{6})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.e.b \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
2646.2.e.c \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots\)
2646.2.e.d \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.e.e \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(0\) \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.e.f \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.g \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.h \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+q^{8}+\cdots\)
2646.2.e.i \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+q^{8}+(2+\cdots)q^{10}+\cdots\)
2646.2.e.j \(2\) \(21.128\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(0\) \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+q^{8}+(3+\cdots)q^{10}+\cdots\)
2646.2.e.k \(4\) \(21.128\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-4\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{8}+\cdots\)
2646.2.e.l \(4\) \(21.128\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-4\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{8}+(-\beta _{1}+\cdots)q^{10}+\cdots\)
2646.2.e.m \(4\) \(21.128\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(-3\) \(0\) \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+q^{8}+\cdots\)
2646.2.e.n \(4\) \(21.128\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(3\) \(0\) \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{8}+(\beta _{1}+\cdots)q^{10}+\cdots\)
2646.2.e.o \(6\) \(21.128\) 6.0.309123.1 None \(-6\) \(0\) \(-5\) \(0\) \(q-q^{2}+q^{4}+(-2+2\beta _{4}-\beta _{5})q^{5}+\cdots\)
2646.2.e.p \(6\) \(21.128\) 6.0.309123.1 None \(6\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
2646.2.e.q \(8\) \(21.128\) \(\Q(\zeta_{24})\) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-2\zeta_{24}^{7}q^{5}-q^{8}+2\zeta_{24}^{7}q^{10}+\cdots\)
2646.2.e.r \(8\) \(21.128\) 8.0.3317760000.3 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{7}q^{5}-q^{8}-\beta _{7}q^{10}+\cdots\)
2646.2.e.s \(8\) \(21.128\) 8.0.\(\cdots\).2 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{4}q^{5}+q^{8}-\beta _{4}q^{10}+\cdots\)
2646.2.e.t \(8\) \(21.128\) \(\Q(\zeta_{24})\) None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\zeta_{24}^{7}q^{5}+q^{8}-\zeta_{24}^{7}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)