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 Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2592.2.i.a 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) 288.2.a.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-4\zeta_{6}q^{5}+6\zeta_{6}q^{13}+8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.b 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 96.2.a.a \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.c 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.a \(0\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.d 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.b \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.e 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) 32.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-2\zeta_{6}q^{5}-6\zeta_{6}q^{13}-2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.f 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.b \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.g 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.a \(0\) \(0\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.h 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 96.2.a.a \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.i 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.e \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.j 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 2592.2.a.c \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.k 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 2592.2.a.c \(0\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.l 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.e \(0\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.m 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.e \(0\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.n 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 2592.2.a.c \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.o 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 2592.2.a.c \(0\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.p 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.e \(0\) \(0\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.q 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 96.2.a.a \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.r 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.a \(0\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.s 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.b \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.t 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) 32.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{5}-6\zeta_{6}q^{13}+2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.u 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.b \(0\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.v 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 864.2.a.a \(0\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.w 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) None 96.2.a.a \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.x 2592.i 9.c $2$ $20.697$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) 288.2.a.a \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+4\zeta_{6}q^{5}+6\zeta_{6}q^{13}-8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.y 2592.i 9.c $4$ $20.697$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) 2592.2.a.i \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-3\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.z 2592.i 9.c $4$ $20.697$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 2592.2.a.m \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+\beta _{2}q^{11}+\cdots\)
2592.2.i.ba 2592.i 9.c $4$ $20.697$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) 2592.2.a.k \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.bb 2592.i 9.c $4$ $20.697$ \(\Q(\sqrt{-3}, \sqrt{13})\) None 864.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bc 2592.i 9.c $4$ $20.697$ \(\Q(\sqrt{-3}, \sqrt{13})\) None 864.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bd 2592.i 9.c $4$ $20.697$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 2592.2.a.m \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+\beta _{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
2592.2.i.be 2592.i 9.c $4$ $20.697$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) 2592.2.a.k \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
2592.2.i.bf 2592.i 9.c $4$ $20.697$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) 2592.2.a.i \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(-3+\cdots)q^{13}+\cdots\)
2592.2.i.bg 2592.i 9.c $8$ $20.697$ 8.0.49787136.1 None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
2592.2.i.bh 2592.i 9.c $8$ $20.697$ 8.0.49787136.1 None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)

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

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