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Properties

Label 2890.2.a
Level $2890$
Weight $2$
Character orbit 2890.a
Rep. character $\chi_{2890}(1,\cdot)$
Character field $\Q$
Dimension $89$
Newform subspaces $36$
Sturm bound $918$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2890.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(918\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2890))\).

Total New Old
Modular forms 494 89 405
Cusp forms 423 89 334
Eisenstein series 71 0 71

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

\(2\)\(5\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(13\)
\(+\)\(+\)\(-\)$-$\(9\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(9\)
\(-\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(36\)
Minus space\(-\)\(53\)

Trace form

\( 89 q + q^{2} + 89 q^{4} - q^{5} - 8 q^{7} + q^{8} + 89 q^{9} + O(q^{10}) \) \( 89 q + q^{2} + 89 q^{4} - q^{5} - 8 q^{7} + q^{8} + 89 q^{9} - q^{10} + 8 q^{11} - 2 q^{13} + 4 q^{15} + 89 q^{16} + 13 q^{18} - q^{20} + 16 q^{21} + 8 q^{22} + 16 q^{23} + 89 q^{25} + 2 q^{26} - 8 q^{28} + 2 q^{29} + 8 q^{31} + q^{32} + 24 q^{33} + 4 q^{35} + 89 q^{36} + 2 q^{37} + 4 q^{38} + 8 q^{39} - q^{40} + 18 q^{41} + 32 q^{42} + 4 q^{43} + 8 q^{44} + 3 q^{45} + 8 q^{47} + 97 q^{49} + q^{50} - 2 q^{52} + 38 q^{53} + 24 q^{54} + 12 q^{55} - 16 q^{57} + 2 q^{58} + 4 q^{60} - 22 q^{61} - 24 q^{63} + 89 q^{64} - 6 q^{65} - 16 q^{66} - 12 q^{67} - 8 q^{69} - 4 q^{70} - 8 q^{71} + 13 q^{72} - 38 q^{73} - 6 q^{74} + 16 q^{77} + 16 q^{78} + 8 q^{79} - q^{80} + 145 q^{81} - 14 q^{82} + 4 q^{83} + 16 q^{84} + 8 q^{86} - 24 q^{87} + 8 q^{88} + 10 q^{89} - 13 q^{90} - 40 q^{91} + 16 q^{92} + 16 q^{93} - 8 q^{94} + 20 q^{95} + 10 q^{97} - 23 q^{98} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 17
2890.2.a.a 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(-3\) \(-1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-4q^{7}+\cdots\)
2890.2.a.b 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(-3\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-2q^{7}+\cdots\)
2890.2.a.c 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(-3\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}+q^{7}+\cdots\)
2890.2.a.d 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
2890.2.a.e 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
2890.2.a.f 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
2890.2.a.g 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
2890.2.a.h 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(2\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots\)
2890.2.a.i 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(2\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
2890.2.a.j 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(2\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2890.2.a.k 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(3\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}-q^{7}+\cdots\)
2890.2.a.l 2890.a 1.a $1$ $23.077$ \(\Q\) None \(-1\) \(3\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}+4q^{7}+\cdots\)
2890.2.a.m 2890.a 1.a $1$ $23.077$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
2890.2.a.n 2890.a 1.a $1$ $23.077$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
2890.2.a.o 2890.a 1.a $1$ $23.077$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2890.2.a.p 2890.a 1.a $1$ $23.077$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2890.2.a.q 2890.a 1.a $1$ $23.077$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
2890.2.a.r 2890.a 1.a $2$ $23.077$ \(\Q(\sqrt{19}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
2890.2.a.s 2890.a 1.a $2$ $23.077$ \(\Q(\sqrt{19}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots\)
2890.2.a.t 2890.a 1.a $2$ $23.077$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
2890.2.a.u 2890.a 1.a $2$ $23.077$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-2\beta q^{7}+\cdots\)
2890.2.a.v 2890.a 1.a $2$ $23.077$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
2890.2.a.w 2890.a 1.a $3$ $23.077$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2890.2.a.x 2890.a 1.a $3$ $23.077$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2890.2.a.y 2890.a 1.a $3$ $23.077$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(3\beta _{1}-\beta _{2})q^{7}-q^{8}+\cdots\)
2890.2.a.z 2890.a 1.a $3$ $23.077$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2890.2.a.ba 2890.a 1.a $3$ $23.077$ 3.3.1304.1 None \(3\) \(0\) \(-3\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2890.2.a.bb 2890.a 1.a $3$ $23.077$ 3.3.1304.1 None \(3\) \(0\) \(3\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2890.2.a.bc 2890.a 1.a $4$ $23.077$ \(\Q(\zeta_{16})^+\) None \(-4\) \(-4\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
2890.2.a.bd 2890.a 1.a $4$ $23.077$ 4.4.37952.1 None \(-4\) \(-2\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2890.2.a.be 2890.a 1.a $4$ $23.077$ 4.4.37952.1 None \(-4\) \(2\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2890.2.a.bf 2890.a 1.a $4$ $23.077$ \(\Q(\zeta_{16})^+\) None \(-4\) \(4\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
2890.2.a.bg 2890.a 1.a $6$ $23.077$ 6.6.37902897.1 None \(6\) \(0\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2890.2.a.bh 2890.a 1.a $6$ $23.077$ 6.6.37902897.1 None \(6\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2890.2.a.bi 2890.a 1.a $8$ $23.077$ 8.8.\(\cdots\).1 None \(8\) \(-4\) \(-8\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}-q^{5}+\cdots\)
2890.2.a.bj 2890.a 1.a $8$ $23.077$ 8.8.\(\cdots\).1 None \(8\) \(4\) \(8\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 2}\)