Properties

Label 8100.2.d
Level $8100$
Weight $2$
Character orbit 8100.d
Rep. character $\chi_{8100}(649,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $19$
Sturm bound $3240$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8100.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(3240\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).

Total New Old
Modular forms 1728 72 1656
Cusp forms 1512 72 1440
Eisenstein series 216 0 216

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 12 q^{31} - 72 q^{49} + 36 q^{61} + 48 q^{79} - 72 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8100.2.d.a 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-6q^{11}-5iq^{13}-3iq^{17}+\cdots\)
8100.2.d.b 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-3q^{11}-2iq^{13}-5q^{19}+\cdots\)
8100.2.d.c 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-3q^{11}-iq^{13}+6iq^{17}+\cdots\)
8100.2.d.d 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-3q^{11}+2iq^{13}-3iq^{17}+\cdots\)
8100.2.d.e 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-4iq^{13}+6iq^{17}-2q^{19}+\cdots\)
8100.2.d.f 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-4iq^{13}-6iq^{17}-2q^{19}+\cdots\)
8100.2.d.g 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{11}-2iq^{13}-5q^{19}+\cdots\)
8100.2.d.h 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{11}-iq^{13}-6iq^{17}+\cdots\)
8100.2.d.i 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{11}+2iq^{13}+3iq^{17}+\cdots\)
8100.2.d.j 8100.d 5.b $2$ $64.679$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+6q^{11}-5iq^{13}+3iq^{17}+\cdots\)
8100.2.d.k 8100.d 5.b $4$ $64.679$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
8100.2.d.l 8100.d 5.b $4$ $64.679$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{7}+\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots\)
8100.2.d.m 8100.d 5.b $4$ $64.679$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots\)
8100.2.d.n 8100.d 5.b $4$ $64.679$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
8100.2.d.o 8100.d 5.b $6$ $64.679$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4})q^{7}+\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots\)
8100.2.d.p 8100.d 5.b $6$ $64.679$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4})q^{7}-\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots\)
8100.2.d.q 8100.d 5.b $8$ $64.679$ 8.0.4057180416.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{7}+(-1-\beta _{1})q^{11}-\beta _{2}q^{13}+\cdots\)
8100.2.d.r 8100.d 5.b $8$ $64.679$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{7}-\beta _{5}q^{11}-\beta _{1}q^{13}+\beta _{6}q^{17}+\cdots\)
8100.2.d.s 8100.d 5.b $8$ $64.679$ 8.0.4057180416.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{7}+(1+\beta _{1})q^{11}-\beta _{2}q^{13}+(2\beta _{3}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(8100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4050, [\chi])\)\(^{\oplus 2}\)