Properties

Label 4018.2.a
Level 4018
Weight 2
Character orbit a
Rep. character \(\chi_{4018}(1,\cdot)\)
Character field \(\Q\)
Dimension 138
Newforms 47
Sturm bound 1176
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4018.a (trivial)
Character field: \(\Q\)
Newforms: \( 47 \)
Sturm bound: \(1176\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4018))\).

Total New Old
Modular forms 604 138 466
Cusp forms 573 138 435
Eisenstein series 31 0 31

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

\(2\)\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(16\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(64\)
Minus space\(-\)\(74\)

Trace form

\(138q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 138q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 146q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(138q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 138q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 146q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 138q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 16q^{18} \) \(\mathstrut +\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 142q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 146q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 24q^{50} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 56q^{57} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut +\mathstrut 40q^{73} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 14q^{76} \) \(\mathstrut +\mathstrut 186q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 48q^{87} \) \(\mathstrut +\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut +\mathstrut 44q^{90} \) \(\mathstrut -\mathstrut 40q^{93} \) \(\mathstrut +\mathstrut 76q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 66q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\) 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 41
4018.2.a.a \(1\) \(32.084\) \(\Q\) None \(-1\) \(-3\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{8}+\cdots\)
4018.2.a.b \(1\) \(32.084\) \(\Q\) None \(-1\) \(-3\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\)
4018.2.a.c \(1\) \(32.084\) \(\Q\) None \(-1\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
4018.2.a.d \(1\) \(32.084\) \(\Q\) None \(-1\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{8}+\cdots\)
4018.2.a.e \(1\) \(32.084\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.f \(1\) \(32.084\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.g \(1\) \(32.084\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.h \(1\) \(32.084\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.i \(1\) \(32.084\) \(\Q\) None \(-1\) \(2\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-4q^{5}-2q^{6}-q^{8}+\cdots\)
4018.2.a.j \(1\) \(32.084\) \(\Q\) None \(-1\) \(2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{8}+\cdots\)
4018.2.a.k \(1\) \(32.084\) \(\Q\) None \(-1\) \(3\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}-q^{8}+\cdots\)
4018.2.a.l \(1\) \(32.084\) \(\Q\) None \(1\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{8}+\cdots\)
4018.2.a.m \(1\) \(32.084\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
4018.2.a.n \(1\) \(32.084\) \(\Q\) None \(1\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{8}-3q^{9}+4q^{10}+\cdots\)
4018.2.a.o \(1\) \(32.084\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.p \(1\) \(32.084\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.q \(1\) \(32.084\) \(\Q\) None \(1\) \(1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.r \(1\) \(32.084\) \(\Q\) None \(1\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
4018.2.a.s \(1\) \(32.084\) \(\Q\) None \(1\) \(3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}+q^{8}+\cdots\)
4018.2.a.t \(2\) \(32.084\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.u \(2\) \(32.084\) \(\Q(\sqrt{33}) \) None \(-2\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-q^{8}+\cdots\)
4018.2.a.v \(2\) \(32.084\) \(\Q(\sqrt{33}) \) None \(-2\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
4018.2.a.w \(2\) \(32.084\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.x \(2\) \(32.084\) \(\Q(\sqrt{3}) \) None \(2\) \(-4\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+(-1-\beta )q^{5}-2q^{6}+\cdots\)
4018.2.a.y \(2\) \(32.084\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
4018.2.a.z \(2\) \(32.084\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4018.2.a.ba \(2\) \(32.084\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)
4018.2.a.bb \(2\) \(32.084\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
4018.2.a.bc \(2\) \(32.084\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+2\beta )q^{5}+\cdots\)
4018.2.a.bd \(3\) \(32.084\) 3.3.404.1 None \(-3\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.be \(3\) \(32.084\) 3.3.404.1 None \(-3\) \(0\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.bf \(3\) \(32.084\) 3.3.321.1 None \(3\) \(-3\) \(4\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots\)
4018.2.a.bg \(3\) \(32.084\) 3.3.568.1 None \(3\) \(-1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
4018.2.a.bh \(3\) \(32.084\) 3.3.321.1 None \(3\) \(3\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
4018.2.a.bi \(4\) \(32.084\) 4.4.113481.1 None \(-4\) \(-4\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}+q^{6}+\cdots\)
4018.2.a.bj \(4\) \(32.084\) 4.4.11348.1 None \(-4\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
4018.2.a.bk \(4\) \(32.084\) 4.4.113481.1 None \(-4\) \(4\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{3})q^{5}-q^{6}+\cdots\)
4018.2.a.bl \(4\) \(32.084\) 4.4.37108.1 None \(4\) \(-3\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.bm \(4\) \(32.084\) 4.4.37108.1 None \(4\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots\)
4018.2.a.bn \(6\) \(32.084\) 6.6.52046292.1 None \(-6\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{3}q^{6}+\cdots\)
4018.2.a.bo \(6\) \(32.084\) 6.6.52046292.1 None \(-6\) \(1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{3}q^{6}+\cdots\)
4018.2.a.bp \(6\) \(32.084\) 6.6.5163008.1 None \(6\) \(-4\) \(-12\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+q^{4}+\cdots\)
4018.2.a.bq \(6\) \(32.084\) 6.6.5163008.1 None \(6\) \(4\) \(12\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+q^{4}+\cdots\)
4018.2.a.br \(10\) \(32.084\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-4\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots\)
4018.2.a.bs \(10\) \(32.084\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
4018.2.a.bt \(10\) \(32.084\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
4018.2.a.bu \(10\) \(32.084\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2009))\)\(^{\oplus 2}\)