Properties

Label 2592.2.i
Level $2592$
Weight $2$
Character orbit 2592.i
Rep. character $\chi_{2592}(865,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $34$
Sturm bound $864$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 34 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2592, [\chi])\).

Total New Old
Modular forms 960 96 864
Cusp forms 768 96 672
Eisenstein series 192 0 192

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 48 q^{25} - 48 q^{49} - 48 q^{73} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2592, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2592.2.i.a \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q-4\zeta_{6}q^{5}+6\zeta_{6}q^{13}+8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.b \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-4\) \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.c \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-3\) \(q-2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.d \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-1\) \(q-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.e \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}-6\zeta_{6}q^{13}-2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.f \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(1\) \(q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.g \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(3\) \(q-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.h \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.i \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-3\) \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.j \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.k \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(2\) \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.l \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(3\) \(q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.m \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-3\) \(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.n \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.o \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.p \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(3\) \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.q \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-4\) \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.r \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-3\) \(q+2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.s \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-1\) \(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.t \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}-6\zeta_{6}q^{13}+2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.u \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(1\) \(q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.v \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(3\) \(q+2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.w \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(4\) \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.x \(2\) \(20.697\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+4\zeta_{6}q^{5}+6\zeta_{6}q^{13}-8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.y \(4\) \(20.697\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-3\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.z \(4\) \(20.697\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+\beta _{2}q^{11}+\cdots\)
2592.2.i.ba \(4\) \(20.697\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.bb \(4\) \(20.697\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bc \(4\) \(20.697\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bd \(4\) \(20.697\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(2\) \(0\) \(q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+\beta _{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
2592.2.i.be \(4\) \(20.697\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.bf \(4\) \(20.697\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(-3+\cdots)q^{13}+\cdots\)
2592.2.i.bg \(8\) \(20.697\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
2592.2.i.bh \(8\) \(20.697\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)