Properties

Label 8034.2.a
Level 8034
Weight 2
Character orbit a
Rep. character \(\chi_{8034}(1,\cdot)\)
Character field \(\Q\)
Dimension 205
Newforms 30
Sturm bound 2912
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)
Character field: \(\Q\)
Newforms: \( 30 \)
Sturm bound: \(2912\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8034))\).

Total New Old
Modular forms 1464 205 1259
Cusp forms 1449 205 1244
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.

\(2\)\(3\)\(13\)\(103\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(12\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(17\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(85\)
Minus space\(-\)\(120\)

Trace form

\(205q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 205q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 205q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(205q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 205q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 205q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 205q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 203q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 32q^{35} \) \(\mathstrut +\mathstrut 205q^{36} \) \(\mathstrut +\mathstrut 22q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 26q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 36q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 205q^{49} \) \(\mathstrut -\mathstrut 33q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 40q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 205q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 32q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 205q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 90q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 40q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8034))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 13 103
8034.2.a.a \(1\) \(64.152\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
8034.2.a.b \(1\) \(64.152\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
8034.2.a.c \(1\) \(64.152\) \(\Q\) None \(-1\) \(1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
8034.2.a.d \(1\) \(64.152\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-5\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-5q^{7}+\cdots\)
8034.2.a.e \(1\) \(64.152\) \(\Q\) None \(1\) \(-1\) \(-2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
8034.2.a.f \(1\) \(64.152\) \(\Q\) None \(1\) \(-1\) \(4\) \(-5\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-5q^{7}+\cdots\)
8034.2.a.g \(1\) \(64.152\) \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
8034.2.a.h \(1\) \(64.152\) \(\Q\) None \(1\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
8034.2.a.i \(1\) \(64.152\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
8034.2.a.j \(1\) \(64.152\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
8034.2.a.k \(1\) \(64.152\) \(\Q\) None \(1\) \(1\) \(4\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
8034.2.a.l \(2\) \(64.152\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-4\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
8034.2.a.m \(2\) \(64.152\) \(\Q(\sqrt{65}) \) None \(-2\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
8034.2.a.n \(4\) \(64.152\) 4.4.72329.1 None \(4\) \(4\) \(2\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}+q^{6}+\cdots\)
8034.2.a.o \(7\) \(64.152\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-9\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
8034.2.a.p \(8\) \(64.152\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(-8\) \(-6\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{5}+\beta _{7})q^{5}+\cdots\)
8034.2.a.q \(8\) \(64.152\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(-6\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
8034.2.a.r \(9\) \(64.152\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-4\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-\beta _{3}q^{7}+\cdots\)
8034.2.a.s \(10\) \(64.152\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-10\) \(6\) \(-9\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{8})q^{5}+q^{6}+\cdots\)
8034.2.a.t \(11\) \(64.152\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(11\) \(4\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{8}q^{7}+\cdots\)
8034.2.a.u \(11\) \(64.152\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(-11\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{9}q^{5}-q^{6}-\beta _{10}q^{7}+\cdots\)
8034.2.a.v \(11\) \(64.152\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(11\) \(5\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{9}q^{7}+\cdots\)
8034.2.a.w \(12\) \(64.152\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(12\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{11}q^{5}-q^{6}-\beta _{9}q^{7}+\cdots\)
8034.2.a.x \(13\) \(64.152\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(13\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+\beta _{3}q^{7}+\cdots\)
8034.2.a.y \(13\) \(64.152\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(-13\) \(3\) \(5\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{8}q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8034.2.a.z \(14\) \(64.152\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(-14\) \(-3\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+\beta _{6}q^{7}+\cdots\)
8034.2.a.ba \(14\) \(64.152\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(-14\) \(-1\) \(5\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-\beta _{7}q^{7}+\cdots\)
8034.2.a.bb \(14\) \(64.152\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(14\) \(-6\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+\beta _{6}q^{7}+\cdots\)
8034.2.a.bc \(15\) \(64.152\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(-15\) \(-1\) \(5\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-\beta _{12}q^{7}+\cdots\)
8034.2.a.bd \(16\) \(64.152\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(16\) \(5\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{9}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(206))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(309))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(618))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1339))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2678))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\)\(^{\oplus 2}\)