Properties

Label 4014.2.a
Level 4014
Weight 2
Character orbit a
Rep. character \(\chi_{4014}(1,\cdot)\)
Character field \(\Q\)
Dimension 92
Newforms 26
Sturm bound 1344
Trace bound 11

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Defining parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)
Character field: \(\Q\)
Newforms: \( 26 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4014))\).

Total New Old
Modular forms 680 92 588
Cusp forms 665 92 573
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.

\(2\)\(3\)\(223\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(38\)
Minus space\(-\)\(54\)

Trace form

\(92q \) \(\mathstrut +\mathstrut 92q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(92q \) \(\mathstrut +\mathstrut 92q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 92q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 84q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 84q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 92q^{64} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 20q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 223
4014.2.a.a \(1\) \(32.052\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+2q^{11}+\cdots\)
4014.2.a.b \(1\) \(32.052\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
4014.2.a.c \(1\) \(32.052\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots\)
4014.2.a.d \(1\) \(32.052\) \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
4014.2.a.e \(1\) \(32.052\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
4014.2.a.f \(1\) \(32.052\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
4014.2.a.g \(1\) \(32.052\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-2q^{11}+\cdots\)
4014.2.a.h \(1\) \(32.052\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+4q^{13}+\cdots\)
4014.2.a.i \(1\) \(32.052\) \(\Q\) None \(1\) \(0\) \(4\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+4q^{5}-4q^{7}+q^{8}+4q^{10}+\cdots\)
4014.2.a.j \(2\) \(32.052\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-2\beta q^{7}-q^{8}+(-5+\beta )q^{11}+\cdots\)
4014.2.a.k \(2\) \(32.052\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-2\beta q^{5}+q^{8}-2\beta q^{10}+\cdots\)
4014.2.a.l \(2\) \(32.052\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-2\beta q^{7}+q^{8}+(5-\beta )q^{11}+\cdots\)
4014.2.a.m \(3\) \(32.052\) \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(-3\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.n \(3\) \(32.052\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(7\) \(-9\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.o \(3\) \(32.052\) 3.3.257.1 None \(3\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4014.2.a.p \(3\) \(32.052\) 3.3.473.1 None \(3\) \(0\) \(1\) \(9\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta _{2}q^{5}+(3-\beta _{1})q^{7}+q^{8}+\cdots\)
4014.2.a.q \(4\) \(32.052\) 4.4.10273.1 None \(4\) \(0\) \(-2\) \(-5\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
4014.2.a.r \(5\) \(32.052\) 5.5.356173.1 None \(5\) \(0\) \(-5\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.s \(6\) \(32.052\) 6.6.232773917.1 None \(-6\) \(0\) \(-6\) \(5\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
4014.2.a.t \(6\) \(32.052\) 6.6.103354048.1 None \(-6\) \(0\) \(-2\) \(8\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(\beta _{4}-\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4014.2.a.u \(6\) \(32.052\) 6.6.103354048.1 None \(6\) \(0\) \(2\) \(8\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(-\beta _{4}+\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4014.2.a.v \(7\) \(32.052\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-6\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots\)
4014.2.a.w \(7\) \(32.052\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-2\) \(6\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\beta _{6})q^{7}+\cdots\)
4014.2.a.x \(8\) \(32.052\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(6\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+(1+\beta _{5}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4014.2.a.y \(8\) \(32.052\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-6\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta _{5}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4014.2.a.z \(8\) \(32.052\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-4\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 2}\)