Properties

Label 5184.2.a
Level $5184$
Weight $2$
Character orbit 5184.a
Rep. character $\chi_{5184}(1,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $58$
Sturm bound $1728$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(1728\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5184))\).

Total New Old
Modular forms 936 100 836
Cusp forms 793 92 701
Eisenstein series 143 8 135

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.
\(+\)\(+\)\(+\)\(21\)
\(+\)\(-\)\(-\)\(25\)
\(-\)\(+\)\(-\)\(25\)
\(-\)\(-\)\(+\)\(21\)
Plus space\(+\)\(42\)
Minus space\(-\)\(50\)

Trace form

\( 92 q + O(q^{10}) \) \( 92 q - 4 q^{13} + 80 q^{25} + 8 q^{37} + 72 q^{49} - 4 q^{61} - 8 q^{73} - 24 q^{85} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5184))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
5184.2.a.a 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}+5q^{11}+2q^{13}-3q^{17}+\cdots\)
5184.2.a.b 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-4\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}-5q^{11}+2q^{13}-3q^{17}+\cdots\)
5184.2.a.c 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-4q^{7}+q^{13}+3q^{17}+4q^{19}+\cdots\)
5184.2.a.d 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-2q^{7}-6q^{11}-5q^{13}-3q^{17}+\cdots\)
5184.2.a.e 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}-3q^{11}+q^{13}+6q^{17}+\cdots\)
5184.2.a.f 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}+3q^{11}+q^{13}+6q^{17}+\cdots\)
5184.2.a.g 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+2q^{7}+6q^{11}-5q^{13}-3q^{17}+\cdots\)
5184.2.a.h 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+4q^{7}+q^{13}+3q^{17}-4q^{19}+\cdots\)
5184.2.a.i 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+5q^{11}+5q^{13}+2q^{17}+\cdots\)
5184.2.a.j 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
5184.2.a.k 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}+5q^{13}+5q^{17}-8q^{19}+\cdots\)
5184.2.a.l 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}+5q^{13}+5q^{17}+8q^{19}+\cdots\)
5184.2.a.m 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
5184.2.a.n 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-5q^{11}+5q^{13}+2q^{17}+\cdots\)
5184.2.a.o 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}-2q^{13}-3q^{17}-q^{19}+\cdots\)
5184.2.a.p 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+3q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
5184.2.a.q 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\)
5184.2.a.r 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+3q^{11}-2q^{13}-3q^{17}+q^{19}+\cdots\)
5184.2.a.s 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-5q^{11}+5q^{13}-2q^{17}+\cdots\)
5184.2.a.t 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}-q^{13}-3q^{17}+\cdots\)
5184.2.a.u 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+5q^{13}-5q^{17}+8q^{19}+\cdots\)
5184.2.a.v 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+5q^{13}-5q^{17}-8q^{19}+\cdots\)
5184.2.a.w 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
5184.2.a.x 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+5q^{11}+5q^{13}-2q^{17}+\cdots\)
5184.2.a.y 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-4q^{7}+q^{13}-3q^{17}+4q^{19}+\cdots\)
5184.2.a.z 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-2q^{7}+6q^{11}-5q^{13}+3q^{17}+\cdots\)
5184.2.a.ba 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}+3q^{11}+q^{13}-6q^{17}+\cdots\)
5184.2.a.bb 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-3q^{11}+q^{13}-6q^{17}+\cdots\)
5184.2.a.bc 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+2q^{7}-6q^{11}-5q^{13}+3q^{17}+\cdots\)
5184.2.a.bd 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+4q^{7}+q^{13}-3q^{17}-4q^{19}+\cdots\)
5184.2.a.be 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{7}-5q^{11}+2q^{13}+3q^{17}+\cdots\)
5184.2.a.bf 5184.a 1.a $1$ $41.394$ \(\Q\) None \(0\) \(0\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}+5q^{11}+2q^{13}+3q^{17}+\cdots\)
5184.2.a.bg 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bh 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-2+\beta )q^{5}+(-3+2\beta )q^{13}+(4+\cdots)q^{17}+\cdots\)
5184.2.a.bi 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bj 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bk 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+\beta q^{11}-3q^{13}+5q^{17}+\cdots\)
5184.2.a.bl 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+\beta q^{11}+3q^{13}-4q^{17}+\cdots\)
5184.2.a.bm 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(-1+\beta )q^{5}+(3+\beta )q^{13}+(-1+2\beta )q^{17}+\cdots\)
5184.2.a.bn 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1-\beta )q^{7}+(-1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bo 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(-2+\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
5184.2.a.bp 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-1\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(2-\beta )q^{7}+q^{11}+(-2-\beta )q^{13}+\cdots\)
5184.2.a.bq 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-2q^{7}-2\beta q^{11}+q^{13}+3\beta q^{17}+\cdots\)
5184.2.a.br 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+2q^{7}+2\beta q^{11}+q^{13}+3\beta q^{17}+\cdots\)
5184.2.a.bs 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
5184.2.a.bt 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
5184.2.a.bu 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5184.2.a.bv 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}-\beta q^{11}-3q^{13}-5q^{17}+\cdots\)
5184.2.a.bw 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{5}+(3-\beta )q^{13}+(1+2\beta )q^{17}+\cdots\)
5184.2.a.bx 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}+3q^{13}+4q^{17}+\cdots\)
5184.2.a.by 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.bz 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.ca 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(2+\beta )q^{5}+(-3-2\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
5184.2.a.cb 5184.a 1.a $2$ $41.394$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5184.2.a.cc 5184.a 1.a $4$ $41.394$ 4.4.13068.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+\cdots\)
5184.2.a.cd 5184.a 1.a $4$ $41.394$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3})q^{11}+\cdots\)
5184.2.a.ce 5184.a 1.a $4$ $41.394$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)
5184.2.a.cf 5184.a 1.a $4$ $41.394$ 4.4.13068.1 None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\)\(^{\oplus 2}\)