Properties

Label 69.6.a
Level $69$
Weight $6$
Character orbit 69.a
Rep. character $\chi_{69}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $5$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(69))\).

Total New Old
Modular forms 42 18 24
Cusp forms 38 18 20
Eisenstein series 4 0 4

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

\(3\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(11\)

Trace form

\( 18q + 8q^{2} - 18q^{3} + 288q^{4} + 32q^{5} - 72q^{6} + 40q^{7} - 108q^{8} + 1458q^{9} + O(q^{10}) \) \( 18q + 8q^{2} - 18q^{3} + 288q^{4} + 32q^{5} - 72q^{6} + 40q^{7} - 108q^{8} + 1458q^{9} + 372q^{10} - 72q^{12} - 1156q^{13} - 84q^{14} + 396q^{15} + 8680q^{16} - 1488q^{17} + 648q^{18} - 3560q^{19} + 9588q^{20} + 2484q^{21} + 1108q^{22} - 3564q^{24} + 18222q^{25} + 2368q^{26} - 1458q^{27} + 1160q^{28} - 7868q^{29} - 1368q^{30} - 19072q^{31} - 19988q^{32} + 13032q^{33} + 29920q^{34} - 5576q^{35} + 23328q^{36} - 29564q^{37} - 49492q^{38} - 22644q^{39} - 20740q^{40} + 40388q^{41} + 5148q^{42} + 8480q^{43} + 53632q^{44} + 2592q^{45} - 8464q^{46} + 65768q^{47} - 6912q^{48} + 20530q^{49} - 35328q^{50} + 12924q^{51} - 7624q^{52} - 139440q^{53} - 5832q^{54} - 23344q^{55} - 144332q^{56} + 17892q^{57} - 15744q^{58} - 11936q^{59} - 30456q^{60} + 68772q^{61} + 61776q^{62} + 3240q^{63} - 28552q^{64} - 103144q^{65} - 147168q^{66} + 96856q^{67} - 11636q^{68} - 19044q^{69} - 380296q^{70} + 155120q^{71} - 8748q^{72} + 103044q^{73} + 91152q^{74} + 66186q^{75} - 51908q^{76} + 126720q^{77} + 5544q^{78} - 87152q^{79} + 335788q^{80} + 118098q^{81} - 218600q^{82} + 4096q^{83} + 220104q^{84} + 101384q^{85} - 82756q^{86} - 196380q^{87} + 646444q^{88} + 310784q^{89} + 30132q^{90} + 198664q^{91} - 227016q^{93} + 39304q^{94} + 258216q^{95} + 18540q^{96} - 251844q^{97} + 401336q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(69))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 23
69.6.a.a \(2\) \(11.066\) \(\Q(\sqrt{29}) \) None \(0\) \(-18\) \(94\) \(-118\) \(+\) \(-\) \(q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots\)
69.6.a.b \(3\) \(11.066\) 3.3.5333.1 None \(-8\) \(27\) \(-56\) \(-114\) \(-\) \(-\) \(q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots\)
69.6.a.c \(4\) \(11.066\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(4\) \(-36\) \(-122\) \(62\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots\)
69.6.a.d \(4\) \(11.066\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(4\) \(-36\) \(22\) \(-62\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
69.6.a.e \(5\) \(11.066\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(8\) \(45\) \(94\) \(272\) \(-\) \(+\) \(q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(69))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(69)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)