Properties

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

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4014.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 223
4014.2.a.a 4014.a 1.a $1$ $32.052$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+2q^{11}+\cdots\)
4014.2.a.b 4014.a 1.a $1$ $32.052$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
4014.2.a.c 4014.a 1.a $1$ $32.052$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots\)
4014.2.a.d 4014.a 1.a $1$ $32.052$ \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
4014.2.a.e 4014.a 1.a $1$ $32.052$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
4014.2.a.f 4014.a 1.a $1$ $32.052$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
4014.2.a.g 4014.a 1.a $1$ $32.052$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-2q^{11}+\cdots\)
4014.2.a.h 4014.a 1.a $1$ $32.052$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+4q^{13}+\cdots\)
4014.2.a.i 4014.a 1.a $1$ $32.052$ \(\Q\) None \(1\) \(0\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}-4q^{7}+q^{8}+4q^{10}+\cdots\)
4014.2.a.j 4014.a 1.a $2$ $32.052$ \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2\beta q^{7}-q^{8}+(-5+\beta )q^{11}+\cdots\)
4014.2.a.k 4014.a 1.a $2$ $32.052$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2\beta q^{5}+q^{8}-2\beta q^{10}+\cdots\)
4014.2.a.l 4014.a 1.a $2$ $32.052$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2\beta q^{7}+q^{8}+(5-\beta )q^{11}+\cdots\)
4014.2.a.m 4014.a 1.a $3$ $32.052$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.n 4014.a 1.a $3$ $32.052$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(7\) \(-9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.o 4014.a 1.a $3$ $32.052$ 3.3.257.1 None \(3\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4014.2.a.p 4014.a 1.a $3$ $32.052$ 3.3.473.1 None \(3\) \(0\) \(1\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+(3-\beta _{1})q^{7}+q^{8}+\cdots\)
4014.2.a.q 4014.a 1.a $4$ $32.052$ 4.4.10273.1 None \(4\) \(0\) \(-2\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
4014.2.a.r 4014.a 1.a $5$ $32.052$ 5.5.356173.1 None \(5\) \(0\) \(-5\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4014.2.a.s 4014.a 1.a $6$ $32.052$ 6.6.232773917.1 None \(-6\) \(0\) \(-6\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
4014.2.a.t 4014.a 1.a $6$ $32.052$ 6.6.103354048.1 None \(-6\) \(0\) \(-2\) \(8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(\beta _{4}-\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4014.2.a.u 4014.a 1.a $6$ $32.052$ 6.6.103354048.1 None \(6\) \(0\) \(2\) \(8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{4}+\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4014.2.a.v 4014.a 1.a $7$ $32.052$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-6\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots\)
4014.2.a.w 4014.a 1.a $7$ $32.052$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-2\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\beta _{6})q^{7}+\cdots\)
4014.2.a.x 4014.a 1.a $8$ $32.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(6\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{5}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4014.2.a.y 4014.a 1.a $8$ $32.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-6\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{5}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4014.2.a.z 4014.a 1.a $8$ $32.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

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

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