Properties

Label 4030.2.a
Level 4030
Weight 2
Character orbit a
Rep. character \(\chi_{4030}(1,\cdot)\)
Character field \(\Q\)
Dimension 121
Newforms 18
Sturm bound 1344
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)
Character field: \(\Q\)
Newforms: \( 18 \)
Sturm bound: \(1344\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4030))\).

Total New Old
Modular forms 680 121 559
Cusp forms 665 121 544
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.

\(2\)\(5\)\(13\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(51\)
Minus space\(-\)\(70\)

Trace form

\(121q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 121q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 117q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(121q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 121q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 117q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 121q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 121q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 38q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 117q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 73q^{49} \) \(\mathstrut -\mathstrut 3q^{50} \) \(\mathstrut +\mathstrut 40q^{51} \) \(\mathstrut +\mathstrut q^{52} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 24q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 76q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut q^{62} \) \(\mathstrut +\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 121q^{64} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 80q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 64q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut +\mathstrut 177q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 22q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut -\mathstrut 86q^{97} \) \(\mathstrut -\mathstrut 11q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\) 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 13 31
4030.2.a.a \(1\) \(32.180\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
4030.2.a.b \(2\) \(32.180\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+2\beta q^{3}+q^{4}-q^{5}-2\beta q^{6}+\cdots\)
4030.2.a.c \(6\) \(32.180\) 6.6.3081125.1 None \(-6\) \(-1\) \(-6\) \(4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
4030.2.a.d \(6\) \(32.180\) 6.6.3728437.1 None \(-6\) \(-1\) \(6\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}-\beta _{3}q^{6}+\cdots\)
4030.2.a.e \(6\) \(32.180\) 6.6.6550837.1 None \(6\) \(-7\) \(6\) \(-8\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4030.2.a.f \(6\) \(32.180\) 6.6.4418197.1 None \(6\) \(-3\) \(-6\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
4030.2.a.g \(6\) \(32.180\) 6.6.10369693.1 None \(6\) \(-3\) \(6\) \(-10\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4030.2.a.h \(7\) \(32.180\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-1\) \(7\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
4030.2.a.i \(7\) \(32.180\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(3\) \(-7\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
4030.2.a.j \(7\) \(32.180\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(-3\) \(-7\) \(4\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)
4030.2.a.k \(8\) \(32.180\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-1\) \(-8\) \(-8\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
4030.2.a.l \(8\) \(32.180\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(1\) \(8\) \(11\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-\beta _{6}q^{3}+q^{4}+q^{5}+\beta _{6}q^{6}+\cdots\)
4030.2.a.m \(8\) \(32.180\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(5\) \(8\) \(5\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4030.2.a.n \(8\) \(32.180\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-1\) \(-8\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
4030.2.a.o \(8\) \(32.180\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(3\) \(8\) \(7\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
4030.2.a.p \(9\) \(32.180\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-3\) \(-9\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
4030.2.a.q \(9\) \(32.180\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(3\) \(-9\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
4030.2.a.r \(9\) \(32.180\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(3\) \(9\) \(9\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(806))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2015))\)\(^{\oplus 2}\)