Properties

Label 2873.2.a
Level $2873$
Weight $2$
Character orbit 2873.a
Rep. character $\chi_{2873}(1,\cdot)$
Character field $\Q$
Dimension $206$
Newform subspaces $26$
Sturm bound $546$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2873 = 13^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2873.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(546\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2873))\).

Total New Old
Modular forms 286 206 80
Cusp forms 259 206 53
Eisenstein series 27 0 27

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

\(13\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(46\)
\(+\)\(-\)\(-\)\(56\)
\(-\)\(+\)\(-\)\(58\)
\(-\)\(-\)\(+\)\(46\)
Plus space\(+\)\(92\)
Minus space\(-\)\(114\)

Trace form

\( 206 q + 2 q^{2} + 206 q^{4} + 4 q^{5} + 6 q^{8} + 210 q^{9} + O(q^{10}) \) \( 206 q + 2 q^{2} + 206 q^{4} + 4 q^{5} + 6 q^{8} + 210 q^{9} + 4 q^{11} - 12 q^{12} + 4 q^{14} + 4 q^{15} + 206 q^{16} - 2 q^{17} + 6 q^{18} - 16 q^{19} + 24 q^{20} - 4 q^{22} - 16 q^{23} + 4 q^{24} + 214 q^{25} - 12 q^{27} + 12 q^{28} + 4 q^{29} - 16 q^{30} - 4 q^{31} + 14 q^{32} - 20 q^{33} + 2 q^{34} - 8 q^{35} + 194 q^{36} - 4 q^{37} - 8 q^{38} - 36 q^{40} + 8 q^{42} - 28 q^{43} + 28 q^{44} + 40 q^{45} + 20 q^{46} + 16 q^{47} - 12 q^{48} + 194 q^{49} + 22 q^{50} - 4 q^{51} + 12 q^{53} + 28 q^{54} - 4 q^{55} + 8 q^{56} - 20 q^{57} - 8 q^{58} - 4 q^{59} + 16 q^{60} - 8 q^{61} - 16 q^{62} - 20 q^{63} + 194 q^{64} - 16 q^{66} + 24 q^{67} - 6 q^{68} + 24 q^{69} + 4 q^{70} + 8 q^{71} + 54 q^{72} - 4 q^{73} + 24 q^{74} - 28 q^{75} - 60 q^{76} - 8 q^{77} - 12 q^{79} - 28 q^{80} + 198 q^{81} - 24 q^{82} - 52 q^{83} - 20 q^{84} - 24 q^{86} - 20 q^{87} - 56 q^{88} + 4 q^{89} - 76 q^{90} - 96 q^{92} - 28 q^{93} - 80 q^{94} - 44 q^{95} - 56 q^{96} - 34 q^{98} - 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2873))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 13 17
2873.2.a.a 2873.a 1.a $1$ $22.941$ \(\Q\) None \(-1\) \(2\) \(-2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{5}-2q^{6}-2q^{7}+\cdots\)
2873.2.a.b 2873.a 1.a $1$ $22.941$ \(\Q\) None \(1\) \(0\) \(-4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\)
2873.2.a.c 2873.a 1.a $1$ $22.941$ \(\Q\) None \(1\) \(0\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}-3q^{9}+\cdots\)
2873.2.a.d 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
2873.2.a.e 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\)
2873.2.a.f 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
2873.2.a.g 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2q^{3}+q^{4}+2\beta q^{5}+2\beta q^{6}+\cdots\)
2873.2.a.h 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(0\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
2873.2.a.i 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{21}) \) None \(1\) \(1\) \(2\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+(3+\beta )q^{4}+q^{5}+\cdots\)
2873.2.a.j 2873.a 1.a $2$ $22.941$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2873.2.a.k 2873.a 1.a $3$ $22.941$ 3.3.229.1 None \(0\) \(-3\) \(2\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2873.2.a.l 2873.a 1.a $4$ $22.941$ 4.4.8112.1 None \(0\) \(-6\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2873.2.a.m 2873.a 1.a $6$ $22.941$ 6.6.434581.1 None \(-3\) \(6\) \(6\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
2873.2.a.n 2873.a 1.a $6$ $22.941$ 6.6.28134208.1 None \(-1\) \(1\) \(2\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
2873.2.a.o 2873.a 1.a $6$ $22.941$ 6.6.434581.1 None \(3\) \(6\) \(-6\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
2873.2.a.p 2873.a 1.a $7$ $22.941$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(-1\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
2873.2.a.q 2873.a 1.a $7$ $22.941$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(1\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2873.2.a.r 2873.a 1.a $10$ $22.941$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2873.2.a.s 2873.a 1.a $11$ $22.941$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(5\) \(-1\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2873.2.a.t 2873.a 1.a $11$ $22.941$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(5\) \(1\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
2873.2.a.u 2873.a 1.a $12$ $22.941$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+\beta _{2}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
2873.2.a.v 2873.a 1.a $18$ $22.941$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-10\) \(-5\) \(5\) \(-17\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{15}q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
2873.2.a.w 2873.a 1.a $18$ $22.941$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(10\) \(-5\) \(-5\) \(17\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{15}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2873.2.a.x 2873.a 1.a $22$ $22.941$ None \(0\) \(6\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$
2873.2.a.y 2873.a 1.a $24$ $22.941$ None \(-5\) \(1\) \(-11\) \(-33\) $-$ $-$ $\mathrm{SU}(2)$
2873.2.a.z 2873.a 1.a $24$ $22.941$ None \(5\) \(1\) \(11\) \(33\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2873))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2873)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 2}\)