Properties

Label 2805.2.a
Level $2805$
Weight $2$
Character orbit 2805.a
Rep. character $\chi_{2805}(1,\cdot)$
Character field $\Q$
Dimension $105$
Newform subspaces $22$
Sturm bound $864$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2805.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(864\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2805))\).

Total New Old
Modular forms 440 105 335
Cusp forms 425 105 320
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.

\(3\)\(5\)\(11\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(5\)
\(+\)\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(+\)\(-\)\(-\)$+$\(4\)
\(+\)\(-\)\(+\)\(+\)$-$\(7\)
\(+\)\(-\)\(+\)\(-\)$+$\(6\)
\(+\)\(-\)\(-\)\(+\)$+$\(7\)
\(+\)\(-\)\(-\)\(-\)$-$\(8\)
\(-\)\(+\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(6\)
\(-\)\(+\)\(-\)\(-\)$-$\(7\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(9\)
\(-\)\(-\)\(-\)\(+\)$-$\(8\)
\(-\)\(-\)\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(41\)
Minus space\(-\)\(64\)

Trace form

\( 105 q + 3 q^{2} - 7 q^{3} + 103 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} + 15 q^{8} + 105 q^{9} + O(q^{10}) \) \( 105 q + 3 q^{2} - 7 q^{3} + 103 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} + 15 q^{8} + 105 q^{9} + 3 q^{10} + q^{11} - 17 q^{12} - 18 q^{13} + 24 q^{14} + q^{15} + 111 q^{16} + q^{17} + 3 q^{18} + 4 q^{19} + 7 q^{20} - 24 q^{21} - 5 q^{22} + 8 q^{23} + 15 q^{24} + 105 q^{25} + 26 q^{26} - 7 q^{27} + 8 q^{28} + 30 q^{29} + 3 q^{30} + 63 q^{32} + q^{33} + 3 q^{34} + 8 q^{35} + 103 q^{36} - 26 q^{37} + 12 q^{38} - 18 q^{39} + 15 q^{40} - 6 q^{41} + 24 q^{42} - 4 q^{43} + 7 q^{44} + q^{45} + 40 q^{46} + 8 q^{47} - 25 q^{48} + 73 q^{49} + 3 q^{50} + q^{51} + 18 q^{52} - 2 q^{53} + 3 q^{54} + q^{55} + 120 q^{56} - 60 q^{57} + 58 q^{58} + 4 q^{59} + 7 q^{60} - 2 q^{61} + 32 q^{62} - 8 q^{63} + 175 q^{64} - 2 q^{65} + 3 q^{66} - 20 q^{67} + 7 q^{68} + 8 q^{69} + 24 q^{70} + 24 q^{71} + 15 q^{72} - 38 q^{73} + 18 q^{74} - 7 q^{75} + 28 q^{76} + 26 q^{78} - 16 q^{79} - 33 q^{80} + 105 q^{81} + 62 q^{82} - 28 q^{83} - 24 q^{84} + q^{85} - 44 q^{86} - 18 q^{87} - 9 q^{88} + 18 q^{89} + 3 q^{90} + 16 q^{91} - 24 q^{92} - 16 q^{93} - 128 q^{94} + 20 q^{95} + 63 q^{96} - 78 q^{97} - 101 q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11 17
2805.2.a.a 2805.a 1.a $1$ $22.398$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
2805.2.a.b 2805.a 1.a $1$ $22.398$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
2805.2.a.c 2805.a 1.a $1$ $22.398$ \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
2805.2.a.d 2805.a 1.a $1$ $22.398$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
2805.2.a.e 2805.a 1.a $1$ $22.398$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
2805.2.a.f 2805.a 1.a $2$ $22.398$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
2805.2.a.g 2805.a 1.a $4$ $22.398$ 4.4.1957.1 None \(-3\) \(4\) \(4\) \(-11\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(1-\beta _{1}-\beta _{3})q^{4}+\cdots\)
2805.2.a.h 2805.a 1.a $4$ $22.398$ 4.4.725.1 None \(-1\) \(-4\) \(-4\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2805.2.a.i 2805.a 1.a $4$ $22.398$ 4.4.725.1 None \(-1\) \(4\) \(4\) \(-5\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2805.2.a.j 2805.a 1.a $4$ $22.398$ 4.4.12357.1 None \(-1\) \(4\) \(-4\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2805.2.a.k 2805.a 1.a $5$ $22.398$ 5.5.81589.1 None \(-3\) \(5\) \(-5\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2}-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
2805.2.a.l 2805.a 1.a $5$ $22.398$ 5.5.81509.1 None \(2\) \(-5\) \(-5\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-q^{3}+(-\beta _{3}-\beta _{4})q^{4}-q^{5}+\cdots\)
2805.2.a.m 2805.a 1.a $6$ $22.398$ 6.6.225947669.1 None \(0\) \(-6\) \(6\) \(-6\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2805.2.a.n 2805.a 1.a $6$ $22.398$ 6.6.94698456.1 None \(1\) \(6\) \(-6\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(\beta _{2}+\beta _{4})q^{4}-q^{5}+\cdots\)
2805.2.a.o 2805.a 1.a $7$ $22.398$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-7\) \(7\) \(-10\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2805.2.a.p 2805.a 1.a $7$ $22.398$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(11\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+q^{5}+\cdots\)
2805.2.a.q 2805.a 1.a $7$ $22.398$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(7\) \(-7\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2805.2.a.r 2805.a 1.a $7$ $22.398$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(-7\) \(-7\) \(-6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2805.2.a.s 2805.a 1.a $7$ $22.398$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(7\) \(7\) \(10\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2805.2.a.t 2805.a 1.a $8$ $22.398$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-8\) \(-8\) \(-4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2805.2.a.u 2805.a 1.a $8$ $22.398$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(-8\) \(8\) \(9\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2805.2.a.v 2805.a 1.a $9$ $22.398$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(9\) \(9\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 2}\)