Properties

Label 2160.2.a
Level $2160$
Weight $2$
Character orbit 2160.a
Rep. character $\chi_{2160}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $28$
Sturm bound $864$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2160))\).

Total New Old
Modular forms 468 32 436
Cusp forms 397 32 365
Eisenstein series 71 0 71

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.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(14\)
Minus space\(-\)\(18\)

Trace form

\( 32 q + 4 q^{7} + O(q^{10}) \) \( 32 q + 4 q^{7} + 32 q^{25} - 36 q^{31} - 32 q^{43} + 40 q^{49} + 8 q^{61} + 68 q^{67} + 8 q^{73} + 64 q^{79} + 8 q^{85} - 52 q^{91} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2160))\) 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
2160.2.a.a $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ \(q-q^{5}-2q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots\)
2160.2.a.b $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ \(q-q^{5}-2q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
2160.2.a.c $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ \(q-q^{5}-2q^{7}+2q^{13}+3q^{17}-5q^{19}+\cdots\)
2160.2.a.d $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ \(q-q^{5}-2q^{7}+q^{11}+q^{13}+q^{17}+\cdots\)
2160.2.a.e $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ \(q-q^{5}-2q^{7}+4q^{11}-2q^{13}-5q^{17}+\cdots\)
2160.2.a.f $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ \(q-q^{5}+2q^{11}-3q^{17}+q^{19}+3q^{23}+\cdots\)
2160.2.a.g $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ \(q-q^{5}+q^{7}-2q^{11}-5q^{13}+4q^{17}+\cdots\)
2160.2.a.h $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ \(q-q^{5}+q^{7}+6q^{11}-q^{13}+q^{19}+\cdots\)
2160.2.a.i $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ \(q-q^{5}+2q^{7}-6q^{13}+7q^{17}-7q^{19}+\cdots\)
2160.2.a.j $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $+$ \(q-q^{5}+3q^{7}+2q^{11}-5q^{13}-8q^{17}+\cdots\)
2160.2.a.k $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ \(q-q^{5}+4q^{7}-6q^{11}-4q^{13}-3q^{17}+\cdots\)
2160.2.a.l $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ \(q-q^{5}+4q^{7}-2q^{11}+4q^{13}+q^{17}+\cdots\)
2160.2.a.m $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ \(q+q^{5}-2q^{7}-4q^{11}-2q^{13}+5q^{17}+\cdots\)
2160.2.a.n $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ \(q+q^{5}-2q^{7}-q^{11}+q^{13}-q^{17}+\cdots\)
2160.2.a.o $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ \(q+q^{5}-2q^{7}+2q^{13}-3q^{17}-5q^{19}+\cdots\)
2160.2.a.p $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ \(q+q^{5}-2q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots\)
2160.2.a.q $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ \(q+q^{5}-2q^{7}+3q^{11}+5q^{13}+3q^{17}+\cdots\)
2160.2.a.r $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ \(q+q^{5}-2q^{11}+3q^{17}+q^{19}-3q^{23}+\cdots\)
2160.2.a.s $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ \(q+q^{5}+q^{7}-6q^{11}-q^{13}+q^{19}+\cdots\)
2160.2.a.t $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ \(q+q^{5}+q^{7}+2q^{11}-5q^{13}-4q^{17}+\cdots\)
2160.2.a.u $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ \(q+q^{5}+2q^{7}-6q^{13}-7q^{17}-7q^{19}+\cdots\)
2160.2.a.v $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $-$ $-$ \(q+q^{5}+3q^{7}-2q^{11}-5q^{13}+8q^{17}+\cdots\)
2160.2.a.w $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $+$ $+$ $-$ \(q+q^{5}+4q^{7}+2q^{11}+4q^{13}-q^{17}+\cdots\)
2160.2.a.x $1$ $17.248$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ \(q+q^{5}+4q^{7}+6q^{11}-4q^{13}+3q^{17}+\cdots\)
2160.2.a.y $2$ $17.248$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ \(q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(3+\cdots)q^{13}+\cdots\)
2160.2.a.z $2$ $17.248$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ \(q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots\)
2160.2.a.ba $2$ $17.248$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ \(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
2160.2.a.bb $2$ $17.248$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $-$ \(q+q^{5}-\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 2}\)