Properties

Label 4029.2.a
Level 4029
Weight 2
Character orbit a
Rep. character \(\chi_{4029}(1,\cdot)\)
Character field \(\Q\)
Dimension 207
Newforms 12
Sturm bound 960
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(960\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4029))\).

Total New Old
Modular forms 484 207 277
Cusp forms 477 207 270
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.

\(3\)\(17\)\(79\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(22\)
\(+\)\(+\)\(-\)\(-\)\(32\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(25\)
\(-\)\(+\)\(-\)\(+\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(31\)
Plus space\(+\)\(94\)
Minus space\(-\)\(113\)

Trace form

\(207q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 201q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 207q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(207q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 201q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 207q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 177q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 181q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 32q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 5q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 201q^{36} \) \(\mathstrut -\mathstrut 38q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 36q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 56q^{47} \) \(\mathstrut -\mathstrut 31q^{48} \) \(\mathstrut +\mathstrut 199q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 7q^{51} \) \(\mathstrut -\mathstrut 42q^{52} \) \(\mathstrut -\mathstrut 46q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 44q^{59} \) \(\mathstrut +\mathstrut 62q^{60} \) \(\mathstrut -\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 44q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 177q^{64} \) \(\mathstrut -\mathstrut 36q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 7q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 66q^{74} \) \(\mathstrut -\mathstrut 31q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 40q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut +\mathstrut 19q^{79} \) \(\mathstrut -\mathstrut 74q^{80} \) \(\mathstrut +\mathstrut 207q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 116q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut -\mathstrut 68q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 56q^{91} \) \(\mathstrut -\mathstrut 28q^{92} \) \(\mathstrut -\mathstrut 32q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 11q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 17 79
4029.2.a.a \(1\) \(32.172\) \(\Q\) None \(0\) \(1\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-4q^{11}+\cdots\)
4029.2.a.b \(1\) \(32.172\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}+q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
4029.2.a.c \(2\) \(32.172\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
4029.2.a.d \(3\) \(32.172\) 3.3.148.1 None \(0\) \(-3\) \(-5\) \(3\) \(+\) \(-\) \(-\) \(q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
4029.2.a.e \(18\) \(32.172\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-6\) \(18\) \(-5\) \(-13\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots\)
4029.2.a.f \(22\) \(32.172\) None \(1\) \(-22\) \(1\) \(-15\) \(+\) \(-\) \(-\)
4029.2.a.g \(22\) \(32.172\) None \(2\) \(-22\) \(5\) \(-4\) \(+\) \(+\) \(+\)
4029.2.a.h \(25\) \(32.172\) None \(-7\) \(25\) \(-12\) \(-4\) \(-\) \(+\) \(-\)
4029.2.a.i \(25\) \(32.172\) None \(-2\) \(-25\) \(-2\) \(12\) \(+\) \(-\) \(+\)
4029.2.a.j \(25\) \(32.172\) None \(6\) \(25\) \(6\) \(4\) \(-\) \(+\) \(+\)
4029.2.a.k \(31\) \(32.172\) None \(4\) \(31\) \(11\) \(4\) \(-\) \(-\) \(-\)
4029.2.a.l \(32\) \(32.172\) None \(-1\) \(-32\) \(-1\) \(4\) \(+\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4029))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4029)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(237))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1343))\)\(^{\oplus 2}\)