Properties

Label 5328.2.a
Level $5328$
Weight $2$
Character orbit 5328.a
Rep. character $\chi_{5328}(1,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $47$
Sturm bound $1824$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5328.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 47 \)
Sturm bound: \(1824\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5328))\).

Total New Old
Modular forms 936 90 846
Cusp forms 889 90 799
Eisenstein series 47 0 47

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

\(2\)\(3\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(14\)
Plus space\(+\)\(42\)
Minus space\(-\)\(48\)

Trace form

\( 90 q + 4 q^{17} + 14 q^{19} + 18 q^{23} + 98 q^{25} + 8 q^{29} + 2 q^{31} - 12 q^{35} - 4 q^{41} + 22 q^{43} + 98 q^{49} - 8 q^{53} - 4 q^{55} - 10 q^{59} - 24 q^{61} + 16 q^{65} - 36 q^{67} - 40 q^{71}+ \cdots - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5328))\) 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 37
5328.2.a.a 5328.a 1.a $1$ $42.544$ \(\Q\) None 888.2.a.d \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{13}-6q^{23}+11q^{25}+\cdots\)
5328.2.a.b 5328.a 1.a $1$ $42.544$ \(\Q\) None 222.2.a.c \(0\) \(0\) \(-4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}-q^{11}-3q^{13}-3q^{17}+\cdots\)
5328.2.a.c 5328.a 1.a $1$ $42.544$ \(\Q\) None 2664.2.a.b \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+5q^{11}+3q^{13}-q^{17}+\cdots\)
5328.2.a.d 5328.a 1.a $1$ $42.544$ \(\Q\) None 1332.2.a.a \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\)
5328.2.a.e 5328.a 1.a $1$ $42.544$ \(\Q\) None 222.2.a.b \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}+6q^{13}-6q^{17}-8q^{19}+\cdots\)
5328.2.a.f 5328.a 1.a $1$ $42.544$ \(\Q\) None 666.2.a.c \(0\) \(0\) \(-2\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+3q^{7}+5q^{11}-3q^{13}-3q^{17}+\cdots\)
5328.2.a.g 5328.a 1.a $1$ $42.544$ \(\Q\) None 333.2.a.a \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
5328.2.a.h 5328.a 1.a $1$ $42.544$ \(\Q\) None 222.2.a.d \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+q^{11}+q^{13}+3q^{17}-3q^{19}+\cdots\)
5328.2.a.i 5328.a 1.a $1$ $42.544$ \(\Q\) None 888.2.a.b \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-6q^{13}+4q^{17}-4q^{19}+6q^{23}+\cdots\)
5328.2.a.j 5328.a 1.a $1$ $42.544$ \(\Q\) None 444.2.a.a \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{11}-2q^{13}-6q^{19}+8q^{23}+\cdots\)
5328.2.a.k 5328.a 1.a $1$ $42.544$ \(\Q\) None 37.2.a.b \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+3q^{11}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5328.2.a.l 5328.a 1.a $1$ $42.544$ \(\Q\) None 222.2.a.e \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+3q^{11}-q^{13}+3q^{17}+7q^{19}+\cdots\)
5328.2.a.m 5328.a 1.a $1$ $42.544$ \(\Q\) None 296.2.a.b \(0\) \(0\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{7}-3q^{11}-2q^{17}+2q^{19}-6q^{23}+\cdots\)
5328.2.a.n 5328.a 1.a $1$ $42.544$ \(\Q\) None 2664.2.a.b \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-5q^{11}+3q^{13}+q^{17}+\cdots\)
5328.2.a.o 5328.a 1.a $1$ $42.544$ \(\Q\) None 296.2.a.a \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+q^{11}-6q^{13}+4q^{17}+\cdots\)
5328.2.a.p 5328.a 1.a $1$ $42.544$ \(\Q\) None 888.2.a.c \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}-2q^{13}+6q^{17}-4q^{23}+\cdots\)
5328.2.a.q 5328.a 1.a $1$ $42.544$ \(\Q\) None 1332.2.a.a \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots\)
5328.2.a.r 5328.a 1.a $1$ $42.544$ \(\Q\) None 37.2.a.a \(0\) \(0\) \(2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-5q^{11}-2q^{13}+2q^{23}+\cdots\)
5328.2.a.s 5328.a 1.a $1$ $42.544$ \(\Q\) None 666.2.a.c \(0\) \(0\) \(2\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+3q^{7}-5q^{11}-3q^{13}+3q^{17}+\cdots\)
5328.2.a.t 5328.a 1.a $1$ $42.544$ \(\Q\) None 444.2.a.b \(0\) \(0\) \(2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
5328.2.a.u 5328.a 1.a $1$ $42.544$ \(\Q\) None 333.2.a.a \(0\) \(0\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5328.2.a.v 5328.a 1.a $1$ $42.544$ \(\Q\) None 222.2.a.a \(0\) \(0\) \(4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-3q^{7}+5q^{11}+3q^{13}-3q^{17}+\cdots\)
5328.2.a.w 5328.a 1.a $1$ $42.544$ \(\Q\) None 888.2.a.a \(0\) \(0\) \(4\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-3q^{11}-5q^{13}-7q^{17}+\cdots\)
5328.2.a.x 5328.a 1.a $1$ $42.544$ \(\Q\) None 148.2.a.a \(0\) \(0\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+3q^{7}+5q^{11}+6q^{17}-2q^{19}+\cdots\)
5328.2.a.y 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{17}) \) None 666.2.a.h \(0\) \(0\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5328.2.a.z 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{17}) \) None 148.2.a.b \(0\) \(0\) \(-4\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5328.2.a.ba 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{5}) \) None 888.2.a.f \(0\) \(0\) \(-2\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-4q^{7}+(2+2\beta )q^{11}+\cdots\)
5328.2.a.bb 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{3}) \) None 888.2.a.e \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+2q^{7}+(-2+2\beta )q^{11}+\cdots\)
5328.2.a.bc 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{5}) \) None 74.2.a.b \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-3\beta )q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+\cdots\)
5328.2.a.bd 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{6}) \) None 444.2.a.d \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-2q^{7}+(2+2\beta )q^{13}-\beta q^{17}+\cdots\)
5328.2.a.be 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{41}) \) None 888.2.a.h \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5328.2.a.bf 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{13}) \) None 74.2.a.a \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+2\beta )q^{7}-\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
5328.2.a.bg 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{3}) \) None 444.2.a.c \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-2\beta q^{7}-4q^{11}-2\beta q^{13}+\cdots\)
5328.2.a.bh 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{17}) \) None 666.2.a.h \(0\) \(0\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5328.2.a.bi 5328.a 1.a $2$ $42.544$ \(\Q(\sqrt{2}) \) None 888.2.a.g \(0\) \(0\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(2-2\beta )q^{7}-2\beta q^{11}+\cdots\)
5328.2.a.bj 5328.a 1.a $3$ $42.544$ 3.3.148.1 None 111.2.a.a \(0\) \(0\) \(-4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
5328.2.a.bk 5328.a 1.a $3$ $42.544$ 3.3.148.1 None 2664.2.a.n \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5328.2.a.bl 5328.a 1.a $3$ $42.544$ 3.3.316.1 None 888.2.a.i \(0\) \(0\) \(-2\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
5328.2.a.bm 5328.a 1.a $3$ $42.544$ 3.3.568.1 None 888.2.a.j \(0\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{2})q^{11}+\cdots\)
5328.2.a.bn 5328.a 1.a $3$ $42.544$ 3.3.229.1 None 296.2.a.c \(0\) \(0\) \(1\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}-3\beta _{1}q^{11}+\cdots\)
5328.2.a.bo 5328.a 1.a $3$ $42.544$ 3.3.148.1 None 2664.2.a.n \(0\) \(0\) \(2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5328.2.a.bp 5328.a 1.a $4$ $42.544$ 4.4.48389.1 None 296.2.a.d \(0\) \(0\) \(-5\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
5328.2.a.bq 5328.a 1.a $4$ $42.544$ 4.4.27648.1 None 333.2.a.f \(0\) \(0\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}-2q^{7}+2q^{13}+\beta _{2}q^{17}+\cdots\)
5328.2.a.br 5328.a 1.a $4$ $42.544$ 4.4.7168.1 None 1332.2.a.i \(0\) \(0\) \(0\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+(-2-\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots\)
5328.2.a.bs 5328.a 1.a $4$ $42.544$ 4.4.6224.1 None 111.2.a.b \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
5328.2.a.bt 5328.a 1.a $5$ $42.544$ 5.5.935504.1 None 2664.2.a.s \(0\) \(0\) \(-2\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
5328.2.a.bu 5328.a 1.a $5$ $42.544$ 5.5.935504.1 None 2664.2.a.s \(0\) \(0\) \(2\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5328))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5328)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(666))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1332))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2664))\)\(^{\oplus 2}\)