Properties

Label 4017.2.a
Level 4017
Weight 2
Character orbit a
Rep. character \(\chi_{4017}(1,\cdot)\)
Character field \(\Q\)
Dimension 203
Newforms 12
Sturm bound 970
Trace bound 4

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Defining parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(970\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4017))\).

Total New Old
Modular forms 488 203 285
Cusp forms 481 203 278
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.

\(3\)\(13\)\(103\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(24\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(27\)
\(-\)\(+\)\(+\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(32\)
Plus space\(+\)\(90\)
Minus space\(-\)\(113\)

Trace form

\(203q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 213q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 203q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(203q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 213q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 203q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 221q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 189q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 32q^{35} \) \(\mathstrut +\mathstrut 213q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut -\mathstrut 34q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 187q^{49} \) \(\mathstrut +\mathstrut 27q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 38q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 18q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 309q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut +\mathstrut 52q^{76} \) \(\mathstrut +\mathstrut 56q^{77} \) \(\mathstrut -\mathstrut 3q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 106q^{80} \) \(\mathstrut +\mathstrut 203q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut +\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 90q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 72q^{92} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 40q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 13 103
4017.2.a.a \(1\) \(32.076\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
4017.2.a.b \(1\) \(32.076\) \(\Q\) None \(-1\) \(1\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
4017.2.a.c \(1\) \(32.076\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
4017.2.a.d \(2\) \(32.076\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4017.2.a.e \(16\) \(32.076\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(16\) \(-6\) \(-13\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
4017.2.a.f \(19\) \(32.076\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-4\) \(19\) \(-3\) \(-23\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots\)
4017.2.a.g \(24\) \(32.076\) None \(3\) \(-24\) \(3\) \(11\) \(+\) \(+\) \(-\)
4017.2.a.h \(25\) \(32.076\) None \(-4\) \(-25\) \(-5\) \(-7\) \(+\) \(-\) \(-\)
4017.2.a.i \(25\) \(32.076\) None \(-2\) \(-25\) \(-3\) \(-11\) \(+\) \(+\) \(+\)
4017.2.a.j \(25\) \(32.076\) None \(6\) \(-25\) \(7\) \(17\) \(+\) \(-\) \(+\)
4017.2.a.k \(32\) \(32.076\) None \(5\) \(32\) \(7\) \(25\) \(-\) \(-\) \(-\)
4017.2.a.l \(32\) \(32.076\) None \(5\) \(32\) \(1\) \(11\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(309))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1339))\)\(^{\oplus 2}\)