Properties

Label 8820.2.a
Level $8820$
Weight $2$
Character orbit 8820.a
Rep. character $\chi_{8820}(1,\cdot)$
Character field $\Q$
Dimension $69$
Newform subspaces $45$
Sturm bound $4032$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8820.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(4032\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8820))\).

Total New Old
Modular forms 2112 69 2043
Cusp forms 1921 69 1852
Eisenstein series 191 0 191

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(32\)
Minus space\(-\)\(37\)

Trace form

\( 69q - q^{5} + O(q^{10}) \) \( 69q - q^{5} + 8q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + 6q^{23} + 69q^{25} - 2q^{29} - 38q^{37} + 2q^{41} - 38q^{43} - 26q^{47} + 6q^{53} + 8q^{55} + 14q^{61} + 10q^{65} - 58q^{67} - 20q^{71} - 18q^{73} - 24q^{79} - 26q^{83} - 10q^{85} - 6q^{89} - 4q^{95} - 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8820))\) 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 7
8820.2.a.a \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-6q^{11}-2q^{13}-6q^{17}-8q^{19}+\cdots\)
8820.2.a.b \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-6q^{11}+4q^{13}+6q^{17}-2q^{19}+\cdots\)
8820.2.a.c \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}-4q^{11}+2q^{17}+6q^{19}-6q^{23}+\cdots\)
8820.2.a.d \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}-4q^{11}+4q^{13}-2q^{17}-4q^{23}+\cdots\)
8820.2.a.e \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{11}-4q^{13}-2q^{17}-2q^{23}+\cdots\)
8820.2.a.f \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{11}-4q^{13}+6q^{17}-6q^{19}+\cdots\)
8820.2.a.g \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{13}-6q^{17}+4q^{19}-6q^{23}+\cdots\)
8820.2.a.h \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+4q^{13}-6q^{17}-2q^{19}+6q^{23}+\cdots\)
8820.2.a.i \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{11}+5q^{13}+q^{17}+6q^{19}+\cdots\)
8820.2.a.j \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{11}+q^{13}+4q^{17}-q^{19}+\cdots\)
8820.2.a.k \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{11}+6q^{13}+2q^{17}+9q^{23}+\cdots\)
8820.2.a.l \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{11}-7q^{13}-6q^{17}-3q^{19}+\cdots\)
8820.2.a.m \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+4q^{11}-4q^{13}-2q^{17}+4q^{23}+\cdots\)
8820.2.a.n \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+5q^{11}+3q^{13}-q^{17}-6q^{19}+\cdots\)
8820.2.a.o \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+6q^{11}+6q^{17}-4q^{19}-6q^{23}+\cdots\)
8820.2.a.p \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-6q^{11}+2q^{13}+6q^{17}+8q^{19}+\cdots\)
8820.2.a.q \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}-4q^{11}-4q^{13}+2q^{17}-4q^{23}+\cdots\)
8820.2.a.r \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-3q^{11}+q^{13}-3q^{17}-2q^{19}+\cdots\)
8820.2.a.s \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots\)
8820.2.a.t \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{11}+4q^{13}+2q^{17}-2q^{23}+\cdots\)
8820.2.a.u \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+4q^{13}+6q^{17}-2q^{19}-6q^{23}+\cdots\)
8820.2.a.v \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{11}-5q^{13}-q^{17}-6q^{19}+\cdots\)
8820.2.a.w \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{11}-6q^{13}-2q^{17}+9q^{23}+\cdots\)
8820.2.a.x \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
8820.2.a.y \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{11}-q^{13}-4q^{17}+q^{19}+\cdots\)
8820.2.a.z \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+4q^{11}-2q^{17}+6q^{19}+6q^{23}+\cdots\)
8820.2.a.ba \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+4q^{11}+4q^{13}+2q^{17}+4q^{23}+\cdots\)
8820.2.a.bb \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{11}+7q^{13}+6q^{17}+3q^{19}+\cdots\)
8820.2.a.bc \(1\) \(70.428\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+6q^{11}-6q^{17}+4q^{19}-6q^{23}+\cdots\)
8820.2.a.bd \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(-2+2\beta )q^{11}-2\beta q^{17}-\beta q^{19}+\cdots\)
8820.2.a.be \(2\) \(70.428\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(-1+\beta )q^{11}-\beta q^{13}+(-1+\cdots)q^{17}+\cdots\)
8820.2.a.bf \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+\beta q^{11}+(1-\beta )q^{13}+\beta q^{17}+\cdots\)
8820.2.a.bg \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(1+2\beta )q^{11}+(-5+\beta )q^{13}+\cdots\)
8820.2.a.bh \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{11}+2\beta q^{13}+(-4+2\beta )q^{17}+\cdots\)
8820.2.a.bi \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+(-2+2\beta )q^{11}+2\beta q^{17}+\beta q^{19}+\cdots\)
8820.2.a.bj \(2\) \(70.428\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+(-1+\beta )q^{11}+\beta q^{13}+(1-\beta )q^{17}+\cdots\)
8820.2.a.bk \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+\beta q^{11}+(-1+\beta )q^{13}-\beta q^{17}+\cdots\)
8820.2.a.bl \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+(1+2\beta )q^{11}+(5-\beta )q^{13}+(-5+\cdots)q^{17}+\cdots\)
8820.2.a.bm \(2\) \(70.428\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{11}-2\beta q^{13}+(4-2\beta )q^{17}+\cdots\)
8820.2.a.bn \(3\) \(70.428\) 3.3.404.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(-1+\beta _{2})q^{11}+(-2+\beta _{2})q^{13}+\cdots\)
8820.2.a.bo \(3\) \(70.428\) 3.3.404.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+(1-\beta _{2})q^{11}+(2-\beta _{2})q^{13}+\cdots\)
8820.2.a.bp \(3\) \(70.428\) 3.3.404.1 None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1+\beta _{2})q^{11}+(2-\beta _{2})q^{13}+\cdots\)
8820.2.a.bq \(3\) \(70.428\) 3.3.404.1 None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+(1-\beta _{2})q^{11}+(-2+\beta _{2})q^{13}+\cdots\)
8820.2.a.br \(4\) \(70.428\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(\beta _{1}+\beta _{2})q^{11}+(-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
8820.2.a.bs \(4\) \(70.428\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+(\beta _{1}+\beta _{2})q^{11}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8820))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8820)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\)\(^{\oplus 2}\)