Properties

Label 2592.2.a
Level $2592$
Weight $2$
Character orbit 2592.a
Rep. character $\chi_{2592}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $24$
Sturm bound $864$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(864\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2592))\).

Total New Old
Modular forms 480 48 432
Cusp forms 385 48 337
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(+\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(22\)
Minus space\(-\)\(26\)

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 48 q^{25} - 24 q^{37} + 48 q^{49} - 24 q^{61} + 24 q^{73} - 24 q^{85} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
2592.2.a.a 2592.a 1.a $1$ $20.697$ \(\Q\) None 288.2.i.a \(0\) \(0\) \(-4\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}+5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.b 2592.a 1.a $1$ $20.697$ \(\Q\) None 288.2.i.a \(0\) \(0\) \(-4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}-5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.c 2592.a 1.a $1$ $20.697$ \(\Q\) None 2592.2.a.c \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.d 2592.a 1.a $1$ $20.697$ \(\Q\) None 2592.2.a.c \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.e 2592.a 1.a $1$ $20.697$ \(\Q\) None 2592.2.a.c \(0\) \(0\) \(1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.f 2592.a 1.a $1$ $20.697$ \(\Q\) None 2592.2.a.c \(0\) \(0\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.g 2592.a 1.a $1$ $20.697$ \(\Q\) None 288.2.i.a \(0\) \(0\) \(4\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{7}-5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.h 2592.a 1.a $1$ $20.697$ \(\Q\) None 288.2.i.a \(0\) \(0\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}+5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.i 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) 2592.2.a.i \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-2+\beta )q^{5}+(3-2\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
2592.2.a.j 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 288.2.i.c \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.k 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) 2592.2.a.k \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+(-1+\beta )q^{5}+(-3-\beta )q^{13}+(1-2\beta )q^{17}+\cdots\)
2592.2.a.l 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) None 288.2.i.d \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-\beta q^{11}-3q^{13}+4q^{17}+\cdots\)
2592.2.a.m 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 2592.2.a.m \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-\beta q^{11}+3q^{13}-5q^{17}+\cdots\)
2592.2.a.n 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 288.2.i.c \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.o 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 288.2.i.c \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
2592.2.a.p 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) None 288.2.i.d \(0\) \(0\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}-3q^{13}-4q^{17}+\cdots\)
2592.2.a.q 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) 2592.2.a.k \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{5}+(-3+\beta )q^{13}+(-1-2\beta )q^{17}+\cdots\)
2592.2.a.r 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 2592.2.a.m \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}+3q^{13}+5q^{17}+\cdots\)
2592.2.a.s 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None 288.2.i.c \(0\) \(0\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1+2\beta )q^{13}+\cdots\)
2592.2.a.t 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) 2592.2.a.i \(0\) \(0\) \(4\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q+(2+\beta )q^{5}+(3+2\beta )q^{13}+(4+\beta )q^{17}+\cdots\)
2592.2.a.u 2592.a 1.a $4$ $20.697$ 4.4.13068.1 None 288.2.i.f \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+\cdots\)
2592.2.a.v 2592.a 1.a $4$ $20.697$ \(\Q(\sqrt{3}, \sqrt{7})\) None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{3})q^{11}+\cdots\)
2592.2.a.w 2592.a 1.a $4$ $20.697$ \(\Q(\sqrt{3}, \sqrt{7})\) None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)
2592.2.a.x 2592.a 1.a $4$ $20.697$ 4.4.13068.1 None 288.2.i.f \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2592)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 2}\)