Properties

Label 8280.2.a
Level $8280$
Weight $2$
Character orbit 8280.a
Rep. character $\chi_{8280}(1,\cdot)$
Character field $\Q$
Dimension $110$
Newform subspaces $49$
Sturm bound $3456$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 49 \)
Sturm bound: \(3456\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8280))\).

Total New Old
Modular forms 1760 110 1650
Cusp forms 1697 110 1587
Eisenstein series 63 0 63

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

\(2\)\(3\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(50\)
Minus space\(-\)\(60\)

Trace form

\( 110 q - 8 q^{7} + O(q^{10}) \) \( 110 q - 8 q^{7} + 4 q^{11} - 12 q^{13} - 20 q^{17} - 20 q^{19} + 110 q^{25} - 8 q^{29} + 16 q^{31} - 12 q^{35} - 8 q^{37} - 12 q^{41} + 4 q^{43} + 94 q^{49} + 24 q^{53} - 4 q^{59} + 16 q^{61} - 28 q^{67} + 20 q^{73} + 16 q^{77} - 20 q^{83} - 4 q^{85} - 36 q^{89} - 8 q^{91} - 8 q^{95} + 44 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8280))\) 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 23
8280.2.a.a \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-3q^{7}+4q^{11}-3q^{17}-4q^{19}+\cdots\)
8280.2.a.b \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}-2q^{7}-2q^{13}-6q^{17}+q^{23}+\cdots\)
8280.2.a.c \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}-2q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
8280.2.a.d \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-2q^{7}+q^{13}-q^{23}+q^{25}+\cdots\)
8280.2.a.e \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{11}-5q^{13}+4q^{17}-2q^{19}+\cdots\)
8280.2.a.f \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{11}-6q^{17}+8q^{19}+q^{23}+\cdots\)
8280.2.a.g \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
8280.2.a.h \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+4q^{11}+4q^{13}+4q^{17}+4q^{19}+\cdots\)
8280.2.a.i \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+q^{7}-4q^{13}+q^{17}-q^{23}+\cdots\)
8280.2.a.j \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+q^{7}+6q^{11}-2q^{13}+3q^{17}+\cdots\)
8280.2.a.k \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
8280.2.a.l \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{7}+2q^{11}+2q^{13}+8q^{17}+\cdots\)
8280.2.a.m \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-2q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
8280.2.a.n \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-2q^{7}-2q^{13}+6q^{17}-q^{23}+\cdots\)
8280.2.a.o \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}+q^{13}+4q^{17}-4q^{19}+\cdots\)
8280.2.a.p \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}-4q^{11}+2q^{13}-2q^{17}+q^{23}+\cdots\)
8280.2.a.q \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-4q^{11}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
8280.2.a.r \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{13}+6q^{17}+q^{23}+q^{25}+\cdots\)
8280.2.a.s \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+2q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
8280.2.a.t \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+3q^{7}+2q^{11}+2q^{13}+q^{17}+\cdots\)
8280.2.a.u \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+3q^{7}+6q^{11}-2q^{13}-3q^{17}+\cdots\)
8280.2.a.v \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots\)
8280.2.a.w \(1\) \(66.116\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}+6q^{11}-4q^{13}-2q^{17}+\cdots\)
8280.2.a.x \(2\) \(66.116\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+(-1+2\beta )q^{7}+\beta q^{11}+(2-\beta )q^{13}+\cdots\)
8280.2.a.y \(2\) \(66.116\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-q^{7}+(2-3\beta )q^{11}+(-4-\beta )q^{13}+\cdots\)
8280.2.a.z \(2\) \(66.116\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}-4q^{11}+(-2+2\beta )q^{13}+\cdots\)
8280.2.a.ba \(2\) \(66.116\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+(1+\beta )q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
8280.2.a.bb \(2\) \(66.116\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+2\beta q^{7}+4q^{11}+(2-\beta )q^{13}+\cdots\)
8280.2.a.bc \(2\) \(66.116\) \(\Q(\sqrt{11}) \) None \(0\) \(0\) \(2\) \(-6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-3q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
8280.2.a.bd \(2\) \(66.116\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+(-1-\beta )q^{7}-2q^{11}-2q^{13}+\cdots\)
8280.2.a.be \(2\) \(66.116\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-\beta q^{7}+2\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
8280.2.a.bf \(2\) \(66.116\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-\beta q^{7}+2q^{11}+(-1-\beta )q^{13}+\cdots\)
8280.2.a.bg \(2\) \(66.116\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+(1+\beta )q^{7}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
8280.2.a.bh \(3\) \(66.116\) 3.3.229.1 None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-\beta _{1}q^{7}+(1-\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots\)
8280.2.a.bi \(3\) \(66.116\) 3.3.568.1 None \(0\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
8280.2.a.bj \(3\) \(66.116\) 3.3.2597.1 None \(0\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+(1-\beta _{1})q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
8280.2.a.bk \(3\) \(66.116\) 3.3.568.1 None \(0\) \(0\) \(-3\) \(4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+(1+\beta _{1})q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bl \(3\) \(66.116\) 3.3.229.1 None \(0\) \(0\) \(-3\) \(7\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+(2-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
8280.2.a.bm \(3\) \(66.116\) 3.3.316.1 None \(0\) \(0\) \(3\) \(-6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+(-2+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
8280.2.a.bn \(3\) \(66.116\) 3.3.1436.1 None \(0\) \(0\) \(3\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+(-1+\beta _{2})q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bo \(3\) \(66.116\) 3.3.621.1 None \(0\) \(0\) \(3\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{1}-\beta _{2})q^{11}+\cdots\)
8280.2.a.bp \(3\) \(66.116\) 3.3.568.1 None \(0\) \(0\) \(3\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots\)
8280.2.a.bq \(4\) \(66.116\) 4.4.54764.1 None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
8280.2.a.br \(5\) \(66.116\) 5.5.20087896.1 None \(0\) \(0\) \(-5\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{2})q^{11}+\cdots\)
8280.2.a.bs \(5\) \(66.116\) 5.5.13955077.1 None \(0\) \(0\) \(5\) \(-2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8280.2.a.bt \(6\) \(66.116\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-6\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-\beta _{2}q^{7}+(1+\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots\)
8280.2.a.bu \(6\) \(66.116\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(6\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}-\beta _{2}q^{7}+(-1-\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots\)
8280.2.a.bv \(7\) \(66.116\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-7\) \(-6\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(-1+\beta _{4})q^{7}+\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots\)
8280.2.a.bw \(7\) \(66.116\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(7\) \(-6\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1+\beta _{4})q^{7}-\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4140))\)\(^{\oplus 2}\)