Properties

Label 1014.4.a
Level $1014$
Weight $4$
Character orbit 1014.a
Rep. character $\chi_{1014}(1,\cdot)$
Character field $\Q$
Dimension $77$
Newform subspaces $31$
Sturm bound $728$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1014.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(728\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1014))\).

Total New Old
Modular forms 574 77 497
Cusp forms 518 77 441
Eisenstein series 56 0 56

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

\(2\)\(3\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(11\)
\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(-\)\(-\)$+$\(10\)
\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(-\)$+$\(11\)
\(-\)\(-\)\(+\)$+$\(13\)
\(-\)\(-\)\(-\)$-$\(7\)
Plus space\(+\)\(45\)
Minus space\(-\)\(32\)

Trace form

\( 77 q + 2 q^{2} + 3 q^{3} + 308 q^{4} + 26 q^{5} + 6 q^{6} + 12 q^{7} + 8 q^{8} + 693 q^{9} + O(q^{10}) \) \( 77 q + 2 q^{2} + 3 q^{3} + 308 q^{4} + 26 q^{5} + 6 q^{6} + 12 q^{7} + 8 q^{8} + 693 q^{9} - 12 q^{10} - 124 q^{11} + 12 q^{12} - 32 q^{14} - 66 q^{15} + 1232 q^{16} - 2 q^{17} + 18 q^{18} + 136 q^{19} + 104 q^{20} + 36 q^{21} - 128 q^{23} + 24 q^{24} + 1747 q^{25} + 27 q^{27} + 48 q^{28} + 258 q^{29} - 84 q^{30} + 404 q^{31} + 32 q^{32} + 348 q^{33} + 260 q^{34} - 168 q^{35} + 2772 q^{36} - 410 q^{37} + 664 q^{38} - 48 q^{40} + 350 q^{41} - 264 q^{42} + 724 q^{43} - 496 q^{44} + 234 q^{45} + 352 q^{46} + 128 q^{47} + 48 q^{48} + 3905 q^{49} + 142 q^{50} - 618 q^{51} + 194 q^{53} + 54 q^{54} + 72 q^{55} - 128 q^{56} + 360 q^{57} + 556 q^{58} - 1268 q^{59} - 264 q^{60} - 478 q^{61} - 144 q^{62} + 108 q^{63} + 4928 q^{64} + 168 q^{66} + 224 q^{67} - 8 q^{68} + 384 q^{69} - 2544 q^{70} - 1712 q^{71} + 72 q^{72} - 1454 q^{73} + 2636 q^{74} + 693 q^{75} + 544 q^{76} + 1176 q^{77} + 3908 q^{79} + 416 q^{80} + 6237 q^{81} - 1228 q^{82} - 12 q^{83} + 144 q^{84} + 20 q^{85} + 680 q^{86} - 1914 q^{87} + 374 q^{89} - 108 q^{90} - 512 q^{92} + 348 q^{93} + 1056 q^{94} - 584 q^{95} + 96 q^{96} - 502 q^{97} - 1230 q^{98} - 1116 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1014))\) 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 13
1014.4.a.a 1014.a 1.a $1$ $59.828$ \(\Q\) None \(-2\) \(-3\) \(-7\) \(-16\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-7q^{5}+6q^{6}+\cdots\)
1014.4.a.b 1014.a 1.a $1$ $59.828$ \(\Q\) None \(-2\) \(-3\) \(-6\) \(-20\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-6q^{5}+6q^{6}+\cdots\)
1014.4.a.c 1014.a 1.a $1$ $59.828$ \(\Q\) None \(-2\) \(-3\) \(8\) \(-14\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+8q^{5}+6q^{6}+\cdots\)
1014.4.a.d 1014.a 1.a $1$ $59.828$ \(\Q\) None \(-2\) \(-3\) \(20\) \(32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+20q^{5}+6q^{6}+\cdots\)
1014.4.a.e 1014.a 1.a $1$ $59.828$ \(\Q\) None \(-2\) \(3\) \(-4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-4q^{5}-6q^{6}+\cdots\)
1014.4.a.f 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(-3\) \(-8\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-8q^{5}-6q^{6}+\cdots\)
1014.4.a.g 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(-3\) \(-6\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
1014.4.a.h 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(-3\) \(7\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+7q^{5}-6q^{6}+\cdots\)
1014.4.a.i 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(-3\) \(16\) \(-28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+2^{4}q^{5}-6q^{6}+\cdots\)
1014.4.a.j 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(3\) \(-10\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-10q^{5}+6q^{6}+\cdots\)
1014.4.a.k 1014.a 1.a $1$ $59.828$ \(\Q\) None \(2\) \(3\) \(16\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+2^{4}q^{5}+6q^{6}+\cdots\)
1014.4.a.l 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{61}) \) None \(-4\) \(-6\) \(2\) \(18\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(1+2\beta )q^{5}+\cdots\)
1014.4.a.m 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{673}) \) None \(-4\) \(6\) \(-13\) \(-9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-6-\beta )q^{5}+\cdots\)
1014.4.a.n 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{3}) \) None \(-4\) \(6\) \(12\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(6+\beta )q^{5}-6q^{6}+\cdots\)
1014.4.a.o 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{17}) \) None \(-4\) \(6\) \(18\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots\)
1014.4.a.p 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{61}) \) None \(4\) \(-6\) \(-2\) \(-18\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-1-2\beta )q^{5}+\cdots\)
1014.4.a.q 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{17}) \) None \(4\) \(6\) \(-18\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-9-\beta )q^{5}+\cdots\)
1014.4.a.r 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{3}) \) None \(4\) \(6\) \(-12\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-6+\beta )q^{5}+\cdots\)
1014.4.a.s 1014.a 1.a $2$ $59.828$ \(\Q(\sqrt{673}) \) None \(4\) \(6\) \(13\) \(9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(7-\beta )q^{5}+6q^{6}+\cdots\)
1014.4.a.t 1014.a 1.a $3$ $59.828$ \(\Q(\zeta_{14})^+\) None \(-6\) \(-9\) \(8\) \(28\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(3-3\beta _{1}-2\beta _{2})q^{5}+\cdots\)
1014.4.a.u 1014.a 1.a $3$ $59.828$ 3.3.1106005.1 None \(-6\) \(9\) \(-12\) \(-17\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-4+\beta _{1})q^{5}+\cdots\)
1014.4.a.v 1014.a 1.a $3$ $59.828$ \(\Q(\zeta_{14})^+\) None \(-6\) \(9\) \(2\) \(44\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(5\beta _{1}+3\beta _{2})q^{5}+\cdots\)
1014.4.a.w 1014.a 1.a $3$ $59.828$ \(\Q(\zeta_{14})^+\) None \(6\) \(-9\) \(-8\) \(-28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-5\beta _{1}+3\beta _{2})q^{5}+\cdots\)
1014.4.a.x 1014.a 1.a $3$ $59.828$ \(\Q(\zeta_{14})^+\) None \(6\) \(9\) \(-2\) \(-44\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-5\beta _{1}-3\beta _{2})q^{5}+\cdots\)
1014.4.a.y 1014.a 1.a $3$ $59.828$ 3.3.1106005.1 None \(6\) \(9\) \(12\) \(17\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(4-\beta _{1})q^{5}+\cdots\)
1014.4.a.z 1014.a 1.a $4$ $59.828$ 4.4.30907152.1 None \(-8\) \(-12\) \(-8\) \(-22\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-2-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.a.ba 1014.a 1.a $4$ $59.828$ 4.4.30907152.1 None \(8\) \(-12\) \(8\) \(22\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.a.bb 1014.a 1.a $6$ $59.828$ 6.6.\(\cdots\).1 None \(-12\) \(-18\) \(-7\) \(-13\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
1014.4.a.bc 1014.a 1.a $6$ $59.828$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(18\) \(3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1014.4.a.bd 1014.a 1.a $6$ $59.828$ 6.6.\(\cdots\).1 None \(12\) \(-18\) \(7\) \(13\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(1-\beta _{4})q^{5}+\cdots\)
1014.4.a.be 1014.a 1.a $6$ $59.828$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(-3\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-1+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1014))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1014)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)