Properties

Label 8030.2.a
Level 8030
Weight 2
Character orbit a
Rep. character \(\chi_{8030}(1,\cdot)\)
Character field \(\Q\)
Dimension 241
Newforms 38
Sturm bound 2664
Trace bound 7

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Defining parameters

Level: \( N \) = \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8030.a (trivial)
Character field: \(\Q\)
Newforms: \( 38 \)
Sturm bound: \(2664\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8030))\).

Total New Old
Modular forms 1340 241 1099
Cusp forms 1325 241 1084
Eisenstein series 15 0 15

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

\(2\)\(5\)\(11\)\(73\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(20\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(17\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(17\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(18\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(101\)
Minus space\(-\)\(140\)

Trace form

\(241q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 241q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 245q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(241q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 241q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 245q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 241q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 241q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 40q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 245q^{36} \) \(\mathstrut +\mathstrut 22q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 241q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut +\mathstrut 40q^{51} \) \(\mathstrut +\mathstrut 14q^{52} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut +\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 34q^{58} \) \(\mathstrut +\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 104q^{63} \) \(\mathstrut +\mathstrut 241q^{64} \) \(\mathstrut +\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 18q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 13q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut +\mathstrut 265q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 28q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut -\mathstrut 3q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 48q^{93} \) \(\mathstrut -\mathstrut 56q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut +\mathstrut 57q^{98} \) \(\mathstrut +\mathstrut 13q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8030))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 11 73
8030.2.a.a \(1\) \(64.120\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
8030.2.a.b \(1\) \(64.120\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
8030.2.a.c \(1\) \(64.120\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
8030.2.a.d \(1\) \(64.120\) \(\Q\) None \(-1\) \(1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
8030.2.a.e \(1\) \(64.120\) \(\Q\) None \(-1\) \(3\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
8030.2.a.f \(1\) \(64.120\) \(\Q\) None \(-1\) \(3\) \(-1\) \(5\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+5q^{7}+\cdots\)
8030.2.a.g \(1\) \(64.120\) \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
8030.2.a.h \(1\) \(64.120\) \(\Q\) None \(1\) \(-2\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
8030.2.a.i \(1\) \(64.120\) \(\Q\) None \(1\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
8030.2.a.j \(1\) \(64.120\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
8030.2.a.k \(2\) \(64.120\) \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.l \(2\) \(64.120\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.m \(2\) \(64.120\) \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.n \(2\) \(64.120\) \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.o \(2\) \(64.120\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
8030.2.a.p \(2\) \(64.120\) \(\Q(\sqrt{13}) \) None \(2\) \(-1\) \(-2\) \(5\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
8030.2.a.q \(2\) \(64.120\) \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(-2\) \(-5\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.r \(3\) \(64.120\) 3.3.316.1 None \(-3\) \(-1\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.s \(3\) \(64.120\) 3.3.229.1 None \(-3\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.t \(3\) \(64.120\) 3.3.229.1 None \(3\) \(-2\) \(3\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.u \(4\) \(64.120\) 4.4.3981.1 None \(4\) \(-1\) \(4\) \(-12\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}+\beta _{3}q^{6}+\cdots\)
8030.2.a.v \(5\) \(64.120\) 5.5.216637.1 None \(5\) \(-5\) \(5\) \(-8\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.w \(6\) \(64.120\) 6.6.47685496.1 None \(-6\) \(-1\) \(-6\) \(6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.x \(6\) \(64.120\) 6.6.32730625.1 None \(-6\) \(2\) \(-6\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
8030.2.a.y \(6\) \(64.120\) 6.6.80296592.1 None \(6\) \(-3\) \(6\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.z \(7\) \(64.120\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-2\) \(7\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.ba \(7\) \(64.120\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(2\) \(7\) \(-7\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
8030.2.a.bb \(8\) \(64.120\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-3\) \(-8\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bc \(11\) \(64.120\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-5\) \(11\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bd \(14\) \(64.120\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(6\) \(-14\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.be \(15\) \(64.120\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(3\) \(15\) \(7\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bf \(15\) \(64.120\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(-4\) \(-15\) \(-6\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bg \(15\) \(64.120\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(7\) \(-15\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bh \(17\) \(64.120\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-17\) \(-1\) \(-17\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bi \(17\) \(64.120\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-17\) \(7\) \(17\) \(9\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bj \(18\) \(64.120\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-18\) \(-6\) \(-18\) \(-6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bk \(18\) \(64.120\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(18\) \(6\) \(18\) \(12\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bl \(19\) \(64.120\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(19\) \(10\) \(19\) \(8\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(146))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(365))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(730))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(803))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1606))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\)\(^{\oplus 2}\)