Properties

Label 8100.2.a
Level $8100$
Weight $2$
Character orbit 8100.a
Rep. character $\chi_{8100}(1,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $31$
Sturm bound $3240$
Trace bound $23$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(3240\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8100))\).

Total New Old
Modular forms 1728 76 1652
Cusp forms 1513 76 1437
Eisenstein series 215 0 215

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.
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(35\)
Minus space\(-\)\(41\)

Trace form

\( 76 q + 2 q^{7} + O(q^{10}) \) \( 76 q + 2 q^{7} - 4 q^{13} - 4 q^{19} - 10 q^{31} - 10 q^{37} + 2 q^{43} + 102 q^{49} - 4 q^{61} - 22 q^{67} - 10 q^{73} + 2 q^{79} - 50 q^{91} - 34 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8100))\) 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 5
8100.2.a.a 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-6q^{11}-5q^{13}+3q^{17}+2q^{19}+\cdots\)
8100.2.a.b 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}+4q^{13}+6q^{17}-7q^{19}+\cdots\)
8100.2.a.c 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{11}-2q^{17}-3q^{19}+4q^{23}+\cdots\)
8100.2.a.d 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{11}+2q^{17}-3q^{19}-4q^{23}+\cdots\)
8100.2.a.e 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+3q^{11}+4q^{13}-6q^{17}-7q^{19}+\cdots\)
8100.2.a.f 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+6q^{11}-5q^{13}-3q^{17}+2q^{19}+\cdots\)
8100.2.a.g 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
8100.2.a.h 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{13}-6q^{17}+2q^{19}-3q^{23}+\cdots\)
8100.2.a.i 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{13}+6q^{17}+2q^{19}+3q^{23}+\cdots\)
8100.2.a.j 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+3q^{11}+q^{13}-6q^{17}-4q^{19}+\cdots\)
8100.2.a.k 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-q^{11}+2q^{17}-3q^{19}-4q^{23}+\cdots\)
8100.2.a.l 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+q^{11}-2q^{17}-3q^{19}+4q^{23}+\cdots\)
8100.2.a.m 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{11}+4q^{13}+5q^{19}-6q^{23}+\cdots\)
8100.2.a.n 8100.a 1.a $1$ $64.679$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}+3q^{11}+4q^{13}+5q^{19}+6q^{23}+\cdots\)
8100.2.a.o 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}+(-2-\beta )q^{11}+(3+\beta )q^{13}+\cdots\)
8100.2.a.p 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}+(2+\beta )q^{11}+(3+\beta )q^{13}+\cdots\)
8100.2.a.q 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}+(-2-\beta )q^{11}+(-3-\beta )q^{13}+\cdots\)
8100.2.a.r 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}+(2+\beta )q^{11}+(-3-\beta )q^{13}+\cdots\)
8100.2.a.s 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}-\beta q^{11}+(-2-2\beta )q^{13}+\cdots\)
8100.2.a.t 8100.a 1.a $2$ $64.679$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}+\beta q^{11}+(-2-2\beta )q^{13}+\cdots\)
8100.2.a.u 8100.a 1.a $3$ $64.679$ 3.3.564.1 None \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{7}+\beta _{2}q^{11}+(-2-\beta _{2})q^{13}+\cdots\)
8100.2.a.v 8100.a 1.a $3$ $64.679$ 3.3.564.1 None \(0\) \(0\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{7}-\beta _{2}q^{11}+(-2-\beta _{2})q^{13}+\cdots\)
8100.2.a.w 8100.a 1.a $4$ $64.679$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{7}-\beta _{3}q^{11}+\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
8100.2.a.x 8100.a 1.a $4$ $64.679$ 4.4.3981.1 None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{7}+(-1-\beta _{2})q^{11}-\beta _{1}q^{13}+\cdots\)
8100.2.a.y 8100.a 1.a $4$ $64.679$ 4.4.3981.1 None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{7}+(1+\beta _{2})q^{11}-\beta _{1}q^{13}+(2+\cdots)q^{17}+\cdots\)
8100.2.a.z 8100.a 1.a $4$ $64.679$ 4.4.3981.1 None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{7}+(-1-\beta _{2})q^{11}+\beta _{1}q^{13}+\cdots\)
8100.2.a.ba 8100.a 1.a $4$ $64.679$ 4.4.3981.1 None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{7}+(1+\beta _{2})q^{11}+\beta _{1}q^{13}+(-2+\cdots)q^{17}+\cdots\)
8100.2.a.bb 8100.a 1.a $4$ $64.679$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
8100.2.a.bc 8100.a 1.a $6$ $64.679$ 6.6.1207701504.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{7}+\beta _{2}q^{11}+(-\beta _{1}+\beta _{4})q^{13}+\cdots\)
8100.2.a.bd 8100.a 1.a $6$ $64.679$ 6.6.1207701504.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{7}-\beta _{2}q^{11}+(-\beta _{1}+\beta _{4})q^{13}+\cdots\)
8100.2.a.be 8100.a 1.a $8$ $64.679$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{7}+(-\beta _{2}+\beta _{7})q^{11}-\beta _{6}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(810))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2025))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4050))\)\(^{\oplus 2}\)