Properties

Label 5400.2.a
Level $5400$
Weight $2$
Character orbit 5400.a
Rep. character $\chi_{5400}(1,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $60$
Sturm bound $2160$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5400.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 60 \)
Sturm bound: \(2160\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5400))\).

Total New Old
Modular forms 1152 76 1076
Cusp forms 1009 76 933
Eisenstein series 143 0 143

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(35\)
Minus space\(-\)\(41\)

Trace form

\( 76 q + 4 q^{7} + O(q^{10}) \) \( 76 q + 4 q^{7} - 6 q^{13} + 2 q^{19} - 10 q^{31} + 26 q^{37} - 20 q^{43} + 68 q^{49} + 22 q^{61} - 6 q^{67} - 8 q^{73} + 10 q^{79} - 18 q^{91} - 20 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5400))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
5400.2.a.a $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ \(q-4q^{7}-4q^{11}+q^{13}-8q^{17}-8q^{19}+\cdots\)
5400.2.a.b $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ \(q-4q^{7}-q^{11}+q^{13}+3q^{17}+2q^{19}+\cdots\)
5400.2.a.c $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ \(q-4q^{7}+q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots\)
5400.2.a.d $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ \(q-4q^{7}+4q^{11}+q^{13}+8q^{17}-8q^{19}+\cdots\)
5400.2.a.e $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ \(q-3q^{7}-5q^{11}-4q^{13}-8q^{17}+2q^{19}+\cdots\)
5400.2.a.f $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $+$ $+$ $+$ \(q-3q^{7}-4q^{11}+6q^{13}-6q^{17}-q^{19}+\cdots\)
5400.2.a.g $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $-$ $+$ $+$ \(q-3q^{7}+4q^{11}+6q^{13}+6q^{17}-q^{19}+\cdots\)
5400.2.a.h $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $-$ $+$ $+$ \(q-3q^{7}+5q^{11}-4q^{13}+8q^{17}+2q^{19}+\cdots\)
5400.2.a.i $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ \(q-2q^{7}-5q^{11}-q^{13}-2q^{17}-8q^{19}+\cdots\)
5400.2.a.j $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ \(q-2q^{7}-4q^{11}+2q^{13}+5q^{17}-5q^{19}+\cdots\)
5400.2.a.k $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ \(q-2q^{7}-3q^{11}-3q^{13}+2q^{17}+4q^{19}+\cdots\)
5400.2.a.l $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ \(q-2q^{7}-2q^{11}+2q^{13}+3q^{17}-q^{19}+\cdots\)
5400.2.a.m $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ \(q-2q^{7}-q^{11}-q^{13}-q^{17}+4q^{19}+\cdots\)
5400.2.a.n $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ \(q-2q^{7}+q^{11}-q^{13}+q^{17}+4q^{19}+\cdots\)
5400.2.a.o $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ \(q-2q^{7}+2q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\)
5400.2.a.p $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ \(q-2q^{7}+3q^{11}-3q^{13}-2q^{17}+4q^{19}+\cdots\)
5400.2.a.q $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ \(q-2q^{7}+4q^{11}+2q^{13}-5q^{17}-5q^{19}+\cdots\)
5400.2.a.r $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ \(q-2q^{7}+5q^{11}-q^{13}+2q^{17}-8q^{19}+\cdots\)
5400.2.a.s $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ \(q-q^{7}-6q^{11}-6q^{13}+2q^{17}+7q^{19}+\cdots\)
5400.2.a.t $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ \(q-q^{7}-2q^{11}-2q^{13}+2q^{17}+q^{19}+\cdots\)
5400.2.a.u $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ \(q-q^{7}+2q^{11}-2q^{13}-2q^{17}+q^{19}+\cdots\)
5400.2.a.v $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ \(q-q^{7}+6q^{11}-6q^{13}-2q^{17}+7q^{19}+\cdots\)
5400.2.a.w $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ \(q-2q^{11}+3q^{17}-q^{19}+3q^{23}-4q^{29}+\cdots\)
5400.2.a.x $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ \(q+2q^{11}-3q^{17}-q^{19}-3q^{23}+4q^{29}+\cdots\)
5400.2.a.y $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ \(q+q^{7}-6q^{11}+6q^{13}-2q^{17}+7q^{19}+\cdots\)
5400.2.a.z $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ \(q+q^{7}-2q^{11}+2q^{13}-2q^{17}+q^{19}+\cdots\)
5400.2.a.ba $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ \(q+q^{7}-2q^{11}+5q^{13}+4q^{17}-5q^{19}+\cdots\)
5400.2.a.bb $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $+$ \(q+q^{7}+2q^{11}+2q^{13}+2q^{17}+q^{19}+\cdots\)
5400.2.a.bc $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $+$ \(q+q^{7}+2q^{11}+5q^{13}-4q^{17}-5q^{19}+\cdots\)
5400.2.a.bd $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ \(q+q^{7}+6q^{11}+6q^{13}+2q^{17}+7q^{19}+\cdots\)
5400.2.a.be $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ \(q+2q^{7}-5q^{11}+q^{13}+2q^{17}-8q^{19}+\cdots\)
5400.2.a.bf $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ \(q+2q^{7}-3q^{11}+3q^{13}-2q^{17}+4q^{19}+\cdots\)
5400.2.a.bg $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ \(q+2q^{7}-2q^{11}-2q^{13}-3q^{17}-q^{19}+\cdots\)
5400.2.a.bh $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ \(q+2q^{7}+6q^{13}-7q^{17}+7q^{19}-7q^{23}+\cdots\)
5400.2.a.bi $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ \(q+2q^{7}+6q^{13}+7q^{17}+7q^{19}+7q^{23}+\cdots\)
5400.2.a.bj $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ \(q+2q^{7}+2q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
5400.2.a.bk $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ \(q+2q^{7}+3q^{11}+3q^{13}+2q^{17}+4q^{19}+\cdots\)
5400.2.a.bl $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ \(q+2q^{7}+5q^{11}+q^{13}-2q^{17}-8q^{19}+\cdots\)
5400.2.a.bm $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $-$ \(q+3q^{7}-4q^{11}-6q^{13}+6q^{17}-q^{19}+\cdots\)
5400.2.a.bn $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $+$ \(q+3q^{7}-4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\)
5400.2.a.bo $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $+$ $-$ $-$ \(q+3q^{7}+4q^{11}-6q^{13}-6q^{17}-q^{19}+\cdots\)
5400.2.a.bp $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $+$ $-$ $+$ \(q+3q^{7}+4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots\)
5400.2.a.bq $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $+$ \(q+4q^{7}-4q^{11}-q^{13}+8q^{17}-8q^{19}+\cdots\)
5400.2.a.br $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ \(q+4q^{7}-2q^{11}-4q^{13}+q^{17}-5q^{19}+\cdots\)
5400.2.a.bs $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $-$ \(q+4q^{7}-q^{11}-q^{13}-3q^{17}+2q^{19}+\cdots\)
5400.2.a.bt $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ \(q+4q^{7}+q^{11}-q^{13}+3q^{17}+2q^{19}+\cdots\)
5400.2.a.bu $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $+$ \(q+4q^{7}+2q^{11}-4q^{13}-q^{17}-5q^{19}+\cdots\)
5400.2.a.bv $1$ $43.119$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ \(q+4q^{7}+4q^{11}-q^{13}-8q^{17}-8q^{19}+\cdots\)
5400.2.a.bw $2$ $43.119$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ \(q-q^{7}+(-2-\beta )q^{11}+(1+2\beta )q^{13}+\cdots\)
5400.2.a.bx $2$ $43.119$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ \(q+(-1-\beta )q^{7}-q^{11}+(-2+\beta )q^{13}+\cdots\)
5400.2.a.by $2$ $43.119$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ \(q+(-1-\beta )q^{7}+q^{11}+(-2+\beta )q^{13}+\cdots\)
5400.2.a.bz $2$ $43.119$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ \(q-q^{7}+(2+\beta )q^{11}+(1+2\beta )q^{13}+2\beta q^{17}+\cdots\)
5400.2.a.ca $2$ $43.119$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ \(q-\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+(-3+\cdots)q^{17}+\cdots\)
5400.2.a.cb $2$ $43.119$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ \(q-\beta q^{7}+(1-\beta )q^{11}-3q^{13}+(3-\beta )q^{17}+\cdots\)
5400.2.a.cc $2$ $43.119$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ \(q+q^{7}+(-2-\beta )q^{11}+(-1-2\beta )q^{13}+\cdots\)
5400.2.a.cd $2$ $43.119$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ \(q+(1+\beta )q^{7}-q^{11}+(2-\beta )q^{13}+(-1+\cdots)q^{17}+\cdots\)
5400.2.a.ce $2$ $43.119$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ \(q+(1+\beta )q^{7}+q^{11}+(2-\beta )q^{13}+(1+\cdots)q^{17}+\cdots\)
5400.2.a.cf $2$ $43.119$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ \(q+q^{7}+(2-\beta )q^{11}+(-1+2\beta )q^{13}+\cdots\)
5400.2.a.cg $4$ $43.119$ \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ \(q+\beta _{1}q^{7}+(-\beta _{1}-2\beta _{2})q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
5400.2.a.ch $4$ $43.119$ \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ \(q+\beta _{1}q^{7}+(\beta _{1}+2\beta _{2})q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2700))\)\(^{\oplus 2}\)