Properties

Label 8022.2.a
Level $8022$
Weight $2$
Character orbit 8022.a
Rep. character $\chi_{8022}(1,\cdot)$
Character field $\Q$
Dimension $189$
Newform subspaces $27$
Sturm bound $3072$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8022.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(3072\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8022))\).

Total New Old
Modular forms 1544 189 1355
Cusp forms 1529 189 1340
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.

\(2\)\(3\)\(7\)\(191\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(13\)
\(+\)\(+\)\(+\)\(-\)$-$\(11\)
\(+\)\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(+\)\(-\)\(-\)$+$\(15\)
\(+\)\(-\)\(+\)\(+\)$-$\(13\)
\(+\)\(-\)\(+\)\(-\)$+$\(11\)
\(+\)\(-\)\(-\)\(+\)$+$\(9\)
\(+\)\(-\)\(-\)\(-\)$-$\(15\)
\(-\)\(+\)\(+\)\(+\)$-$\(13\)
\(-\)\(+\)\(+\)\(-\)$+$\(10\)
\(-\)\(+\)\(-\)\(+\)$+$\(12\)
\(-\)\(+\)\(-\)\(-\)$-$\(11\)
\(-\)\(-\)\(+\)\(+\)$+$\(8\)
\(-\)\(-\)\(+\)\(-\)$-$\(15\)
\(-\)\(-\)\(-\)\(+\)$-$\(17\)
\(-\)\(-\)\(-\)\(-\)$+$\(7\)
Plus space\(+\)\(85\)
Minus space\(-\)\(104\)

Trace form

\( 189 q - 3 q^{2} + q^{3} + 189 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 189 q^{9} + O(q^{10}) \) \( 189 q - 3 q^{2} + q^{3} + 189 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 189 q^{9} - 2 q^{10} - 4 q^{11} + q^{12} - 26 q^{13} + q^{14} - 10 q^{15} + 189 q^{16} - 22 q^{17} - 3 q^{18} - 12 q^{19} - 2 q^{20} + q^{21} + 12 q^{22} - 8 q^{23} + q^{24} + 187 q^{25} - 10 q^{26} + q^{27} + q^{28} - 10 q^{29} - 2 q^{30} - 3 q^{32} - 4 q^{33} - 22 q^{34} + 6 q^{35} + 189 q^{36} + 14 q^{37} + 20 q^{38} - 2 q^{39} - 2 q^{40} - 14 q^{41} + q^{42} + 4 q^{43} - 4 q^{44} - 2 q^{45} - 8 q^{46} - 32 q^{47} + q^{48} + 189 q^{49} - 29 q^{50} + 10 q^{51} - 26 q^{52} - 34 q^{53} + q^{54} - 56 q^{55} + q^{56} + 20 q^{57} + 22 q^{58} - 20 q^{59} - 10 q^{60} + 22 q^{61} + q^{63} + 189 q^{64} - 12 q^{65} - 4 q^{66} - 4 q^{67} - 22 q^{68} + 8 q^{69} + 6 q^{70} - 24 q^{71} - 3 q^{72} - 30 q^{73} + 14 q^{74} - q^{75} - 12 q^{76} - 20 q^{77} + 6 q^{78} - 2 q^{80} + 189 q^{81} - 14 q^{82} - 12 q^{83} + q^{84} - 4 q^{85} + 12 q^{86} - 2 q^{87} + 12 q^{88} + 18 q^{89} - 2 q^{90} + 14 q^{91} - 8 q^{92} - 16 q^{94} + 8 q^{95} + q^{96} + 58 q^{97} - 3 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8022))\) 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 7 191
8022.2.a.a 8022.a 1.a $1$ $64.056$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.b 8022.a 1.a $1$ $64.056$ \(\Q\) None \(-1\) \(-1\) \(3\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.c 8022.a 1.a $1$ $64.056$ \(\Q\) None \(-1\) \(1\) \(-3\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.d 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.e 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
8022.2.a.f 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.g 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.h 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.i 8022.a 1.a $1$ $64.056$ \(\Q\) None \(1\) \(1\) \(3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.j 8022.a 1.a $2$ $64.056$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
8022.2.a.k 8022.a 1.a $2$ $64.056$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
8022.2.a.l 8022.a 1.a $7$ $64.056$ 7.7.118870813.1 None \(7\) \(7\) \(-8\) \(7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
8022.2.a.m 8022.a 1.a $7$ $64.056$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(-3\) \(-7\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2}+\beta _{6})q^{5}+\cdots\)
8022.2.a.n 8022.a 1.a $8$ $64.056$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-8\) \(9\) \(8\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{4})q^{5}+q^{6}+\cdots\)
8022.2.a.o 8022.a 1.a $8$ $64.056$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(2\) \(8\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
8022.2.a.p 8022.a 1.a $9$ $64.056$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-4\) \(9\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.q 8022.a 1.a $9$ $64.056$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(6\) \(-9\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\)
8022.2.a.r 8022.a 1.a $10$ $64.056$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-10\) \(8\) \(10\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
8022.2.a.s 8022.a 1.a $11$ $64.056$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-11\) \(6\) \(-11\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
8022.2.a.t 8022.a 1.a $11$ $64.056$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(11\) \(1\) \(-11\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
8022.2.a.u 8022.a 1.a $11$ $64.056$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(-11\) \(-8\) \(-11\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{4})q^{5}-q^{6}+\cdots\)
8022.2.a.v 8022.a 1.a $13$ $64.056$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(-13\) \(-5\) \(-13\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.w 8022.a 1.a $13$ $64.056$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(13\) \(-2\) \(-13\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
8022.2.a.x 8022.a 1.a $14$ $64.056$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(-14\) \(-10\) \(14\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
8022.2.a.y 8022.a 1.a $14$ $64.056$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(14\) \(-4\) \(-14\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.z 8022.a 1.a $15$ $64.056$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(15\) \(0\) \(15\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.ba 8022.a 1.a $16$ $64.056$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(16\) \(11\) \(16\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(382))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1337))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2674))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\)\(^{\oplus 2}\)