Properties

Label 805.2.a
Level $805$
Weight $2$
Character orbit 805.a
Rep. character $\chi_{805}(1,\cdot)$
Character field $\Q$
Dimension $43$
Newform subspaces $13$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(805))\).

Total New Old
Modular forms 100 43 57
Cusp forms 93 43 50
Eisenstein series 7 0 7

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

\(5\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(18\)
Minus space\(-\)\(25\)

Trace form

\( 43 q + q^{2} + 4 q^{3} + 37 q^{4} - q^{5} + 8 q^{6} - q^{7} + 9 q^{8} + 59 q^{9} + O(q^{10}) \) \( 43 q + q^{2} + 4 q^{3} + 37 q^{4} - q^{5} + 8 q^{6} - q^{7} + 9 q^{8} + 59 q^{9} - 3 q^{10} + 8 q^{12} - 14 q^{13} - 3 q^{14} + 13 q^{16} + 6 q^{17} - 7 q^{18} + 4 q^{19} - 7 q^{20} - 12 q^{22} + 11 q^{23} + 20 q^{24} + 43 q^{25} + 2 q^{26} + 16 q^{27} - 7 q^{28} - 26 q^{29} + 20 q^{30} - 16 q^{31} + 29 q^{32} + 48 q^{33} + 10 q^{34} + 7 q^{35} + 69 q^{36} - 22 q^{37} - 12 q^{38} - 12 q^{39} - 15 q^{40} + 22 q^{41} - 12 q^{42} + 4 q^{43} + 28 q^{44} - 13 q^{45} - 3 q^{46} - 40 q^{47} - 32 q^{48} + 43 q^{49} + q^{50} - 20 q^{51} - 22 q^{52} - 46 q^{53} - 20 q^{54} - 12 q^{55} - 15 q^{56} - 46 q^{58} - 12 q^{59} - 12 q^{60} - 38 q^{61} - 28 q^{62} - 13 q^{63} - 47 q^{64} - 10 q^{65} - 96 q^{66} - 28 q^{67} - 70 q^{68} - 4 q^{69} + q^{70} - 40 q^{71} - 75 q^{72} + 14 q^{73} - 50 q^{74} + 4 q^{75} + 12 q^{76} + 4 q^{77} - 28 q^{78} - 28 q^{79} + q^{80} + 131 q^{81} + 46 q^{82} - 20 q^{83} - 12 q^{84} + 2 q^{85} - 68 q^{86} + 24 q^{87} + 12 q^{88} - 10 q^{89} - 39 q^{90} - 2 q^{91} + 17 q^{92} + 40 q^{93} - 12 q^{94} + 20 q^{95} + 40 q^{96} + 14 q^{97} + q^{98} + 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(805))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 23
805.2.a.a 805.a 1.a $1$ $6.428$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.b 805.a 1.a $1$ $6.428$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.c 805.a 1.a $1$ $6.428$ \(\Q\) None \(2\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
805.2.a.d 805.a 1.a $1$ $6.428$ \(\Q\) None \(2\) \(3\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots\)
805.2.a.e 805.a 1.a $2$ $6.428$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
805.2.a.f 805.a 1.a $3$ $6.428$ \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
805.2.a.g 805.a 1.a $4$ $6.428$ 4.4.2777.1 None \(-2\) \(-5\) \(4\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
805.2.a.h 805.a 1.a $4$ $6.428$ 4.4.22545.1 None \(-1\) \(0\) \(-4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
805.2.a.i 805.a 1.a $4$ $6.428$ 4.4.7537.1 None \(1\) \(4\) \(-4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.j 805.a 1.a $4$ $6.428$ 4.4.2777.1 None \(3\) \(6\) \(4\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
805.2.a.k 805.a 1.a $5$ $6.428$ 5.5.122821.1 None \(-3\) \(-6\) \(5\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
805.2.a.l 805.a 1.a $5$ $6.428$ 5.5.255877.1 None \(-1\) \(-4\) \(-5\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.m 805.a 1.a $8$ $6.428$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(7\) \(8\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)