↑

Properties

Label 1805.2.a
Level $1805$
Weight $2$
Character orbit 1805.a
Rep. character $\chi_{1805}(1,\cdot)$
Character field $\Q$
Dimension $113$
Newform subspaces $23$
Sturm bound $380$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(380\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1805))\).

Total New Old
Modular forms 210 113 97
Cusp forms 171 113 58
Eisenstein series 39 0 39

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

\(5\)\(19\)FrickeDim
\(+\)\(+\)$+$\(23\)
\(+\)\(-\)$-$\(33\)
\(-\)\(+\)$-$\(33\)
\(-\)\(-\)$+$\(24\)
Plus space\(+\)\(47\)
Minus space\(-\)\(66\)

Trace form

\( 113 q + q^{2} - 4 q^{3} + 111 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 109 q^{9} + O(q^{10}) \) \( 113 q + q^{2} - 4 q^{3} + 111 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 109 q^{9} - 3 q^{10} + 4 q^{11} + 4 q^{12} - 10 q^{13} + 12 q^{14} + 119 q^{16} - 6 q^{17} + 29 q^{18} + 7 q^{20} + 16 q^{21} + 12 q^{22} + 12 q^{23} + 20 q^{24} + 113 q^{25} - 6 q^{26} - 4 q^{27} - 4 q^{28} + 6 q^{29} - 4 q^{30} - 8 q^{31} + 9 q^{32} - 12 q^{33} - 14 q^{34} + 4 q^{35} + 83 q^{36} - 14 q^{37} - 4 q^{39} - 15 q^{40} - 14 q^{41} - 28 q^{42} - 20 q^{44} + 5 q^{45} - 12 q^{46} - 48 q^{48} + 89 q^{49} + q^{50} + 32 q^{51} - 22 q^{52} - 6 q^{53} - 20 q^{54} + 12 q^{55} - 4 q^{56} - 10 q^{58} + 20 q^{59} + 16 q^{60} - 26 q^{61} - 60 q^{62} + 123 q^{64} - 6 q^{65} - 8 q^{66} + 16 q^{67} - 14 q^{68} - 16 q^{69} - 4 q^{70} + 24 q^{71} + 65 q^{72} - 38 q^{73} - 54 q^{74} - 4 q^{75} + 32 q^{77} + 16 q^{79} - q^{80} + 97 q^{81} - 18 q^{82} + 24 q^{83} + 24 q^{84} + 2 q^{85} + 24 q^{86} + 44 q^{87} + 16 q^{88} - 6 q^{89} - 39 q^{90} + 16 q^{91} + 8 q^{92} + 40 q^{93} + 52 q^{94} + 4 q^{96} - 50 q^{97} - 23 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\) 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 19
1805.2.a.a 1805.a 1.a $1$ $14.413$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
1805.2.a.b 1805.a 1.a $1$ $14.413$ \(\Q\) None \(0\) \(2\) \(-1\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
1805.2.a.c 1805.a 1.a $2$ $14.413$ \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1805.2.a.d 1805.a 1.a $2$ $14.413$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}-q^{5}-2q^{7}-\beta q^{8}+\cdots\)
1805.2.a.e 1805.a 1.a $2$ $14.413$ \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
1805.2.a.f 1805.a 1.a $3$ $14.413$ 3.3.148.1 None \(-1\) \(-2\) \(3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.g 1805.a 1.a $3$ $14.413$ 3.3.361.1 None \(-1\) \(-1\) \(-3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1805.2.a.h 1805.a 1.a $3$ $14.413$ 3.3.361.1 None \(1\) \(1\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.i 1805.a 1.a $4$ $14.413$ 4.4.7537.1 None \(-1\) \(-3\) \(4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.2.a.j 1805.a 1.a $4$ $14.413$ 4.4.2225.1 None \(-1\) \(-1\) \(4\) \(-11\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3})q^{4}+\cdots\)
1805.2.a.k 1805.a 1.a $4$ $14.413$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{3}-2q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1805.2.a.l 1805.a 1.a $4$ $14.413$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1805.2.a.m 1805.a 1.a $4$ $14.413$ 4.4.7168.1 None \(0\) \(0\) \(4\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.2.a.n 1805.a 1.a $4$ $14.413$ 4.4.2225.1 None \(1\) \(1\) \(4\) \(-11\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.o 1805.a 1.a $4$ $14.413$ 4.4.7537.1 None \(1\) \(3\) \(4\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.2.a.p 1805.a 1.a $4$ $14.413$ 4.4.11344.1 None \(2\) \(-2\) \(-4\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
1805.2.a.q 1805.a 1.a $6$ $14.413$ 6.6.5822000.1 None \(-2\) \(-4\) \(-6\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
1805.2.a.r 1805.a 1.a $6$ $14.413$ 6.6.5822000.1 None \(2\) \(4\) \(-6\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4})q^{3}+\cdots\)
1805.2.a.s 1805.a 1.a $9$ $14.413$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(-9\) \(9\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
1805.2.a.t 1805.a 1.a $9$ $14.413$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-9\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.u 1805.a 1.a $9$ $14.413$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(-9\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.2.a.v 1805.a 1.a $9$ $14.413$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(6\) \(9\) \(9\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
1805.2.a.w 1805.a 1.a $16$ $14.413$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(16\) \(22\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)