Properties

Label 6034.2.a
Level 6034
Weight 2
Character orbit a
Rep. character \(\chi_{6034}(1,\cdot)\)
Character field \(\Q\)
Dimension 215
Newforms 18
Sturm bound 1728
Trace bound 7

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Defining parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)
Character field: \(\Q\)
Newforms: \( 18 \)
Sturm bound: \(1728\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6034))\).

Total New Old
Modular forms 868 215 653
Cusp forms 861 215 646
Eisenstein series 7 0 7

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

\(2\)\(7\)\(431\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(28\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(26\)
\(-\)\(+\)\(+\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(+\)\(23\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(98\)
Minus space\(-\)\(117\)

Trace form

\(215q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 215q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 219q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(215q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 215q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 219q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 215q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 233q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut 3q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 30q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 219q^{36} \) \(\mathstrut +\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 46q^{45} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 215q^{49} \) \(\mathstrut +\mathstrut 13q^{50} \) \(\mathstrut +\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut +\mathstrut 48q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut -\mathstrut q^{56} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 13q^{63} \) \(\mathstrut +\mathstrut 215q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut -\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 191q^{81} \) \(\mathstrut +\mathstrut 38q^{82} \) \(\mathstrut -\mathstrut 64q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut -\mathstrut 34q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 431
6034.2.a.a \(1\) \(48.182\) \(\Q\) None \(-1\) \(-3\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{7}+\cdots\)
6034.2.a.b \(1\) \(48.182\) \(\Q\) None \(-1\) \(-3\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}+q^{7}+\cdots\)
6034.2.a.c \(1\) \(48.182\) \(\Q\) None \(-1\) \(-2\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{7}+\cdots\)
6034.2.a.d \(1\) \(48.182\) \(\Q\) None \(-1\) \(0\) \(-4\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
6034.2.a.e \(1\) \(48.182\) \(\Q\) None \(1\) \(-1\) \(-3\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
6034.2.a.f \(1\) \(48.182\) \(\Q\) None \(1\) \(3\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{7}+\cdots\)
6034.2.a.g \(2\) \(48.182\) \(\Q(\sqrt{5}) \) None \(-2\) \(4\) \(-5\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}+2q^{3}+q^{4}+(-2-\beta )q^{5}-2q^{6}+\cdots\)
6034.2.a.h \(2\) \(48.182\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
6034.2.a.i \(2\) \(48.182\) \(\Q(\sqrt{3}) \) None \(2\) \(4\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
6034.2.a.j \(4\) \(48.182\) 4.4.10273.1 None \(-4\) \(-2\) \(1\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{3}q^{5}+\cdots\)
6034.2.a.k \(20\) \(48.182\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(3\) \(-3\) \(20\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{15}q^{5}-\beta _{1}q^{6}+\cdots\)
6034.2.a.l \(20\) \(48.182\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(-3\) \(-10\) \(-20\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{7})q^{5}+\cdots\)
6034.2.a.m \(21\) \(48.182\) None \(21\) \(-6\) \(-11\) \(21\) \(-\) \(-\) \(+\)
6034.2.a.n \(24\) \(48.182\) None \(-24\) \(7\) \(8\) \(-24\) \(+\) \(+\) \(-\)
6034.2.a.o \(25\) \(48.182\) None \(-25\) \(-4\) \(0\) \(-25\) \(+\) \(+\) \(+\)
6034.2.a.p \(27\) \(48.182\) None \(-27\) \(4\) \(9\) \(27\) \(+\) \(-\) \(+\)
6034.2.a.q \(31\) \(48.182\) None \(31\) \(2\) \(13\) \(31\) \(-\) \(-\) \(-\)
6034.2.a.r \(31\) \(48.182\) None \(31\) \(7\) \(15\) \(-31\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3017))\)\(^{\oplus 2}\)