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Properties

Label 2670.2.a
Level $2670$
Weight $2$
Character orbit 2670.a
Rep. character $\chi_{2670}(1,\cdot)$
Character field $\Q$
Dimension $57$
Newform subspaces $20$
Sturm bound $1080$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2670 = 2 \cdot 3 \cdot 5 \cdot 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2670.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(1080\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2670))\).

Total New Old
Modular forms 548 57 491
Cusp forms 533 57 476
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.

\(2\)\(3\)\(5\)\(89\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(-\)$-$\(7\)
\(+\)\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(-\)$+$\(3\)
\(+\)\(-\)\(+\)\(+\)$-$\(3\)
\(+\)\(-\)\(+\)\(-\)$+$\(3\)
\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(-\)$-$\(5\)
\(-\)\(+\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(+\)\(-\)$+$\(2\)
\(-\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(3\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(6\)
\(-\)\(-\)\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(19\)
Minus space\(-\)\(38\)

Trace form

\( 57 q + q^{2} - 3 q^{3} + 57 q^{4} + q^{5} + q^{6} + q^{8} + 57 q^{9} + O(q^{10}) \) \( 57 q + q^{2} - 3 q^{3} + 57 q^{4} + q^{5} + q^{6} + q^{8} + 57 q^{9} + q^{10} - 4 q^{11} - 3 q^{12} - 18 q^{13} - 8 q^{14} + q^{15} + 57 q^{16} - 14 q^{17} + q^{18} + 12 q^{19} + q^{20} - 4 q^{22} + 8 q^{23} + q^{24} + 57 q^{25} + 14 q^{26} - 3 q^{27} - 2 q^{29} - 3 q^{30} - 16 q^{31} + q^{32} + 4 q^{33} - 6 q^{34} - 8 q^{35} + 57 q^{36} - 10 q^{37} - 12 q^{38} - 18 q^{39} + q^{40} - 22 q^{41} - 8 q^{42} - 4 q^{43} - 4 q^{44} + q^{45} + 16 q^{47} - 3 q^{48} + 41 q^{49} + q^{50} + 18 q^{51} - 18 q^{52} - 10 q^{53} + q^{54} + 4 q^{55} - 8 q^{56} - 4 q^{57} + 6 q^{58} + 12 q^{59} + q^{60} + 22 q^{61} - 16 q^{62} + 57 q^{64} + 14 q^{65} + 4 q^{66} + 4 q^{67} - 14 q^{68} + 24 q^{71} + q^{72} + 42 q^{73} + 6 q^{74} - 3 q^{75} + 12 q^{76} + 64 q^{77} + 14 q^{78} + 8 q^{79} + q^{80} + 57 q^{81} + 10 q^{82} + 4 q^{83} + 2 q^{85} - 20 q^{86} + 22 q^{87} - 4 q^{88} + q^{89} + q^{90} + 32 q^{91} + 8 q^{92} - 24 q^{93} + 8 q^{94} + 4 q^{95} + q^{96} + 2 q^{97} + 25 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2670))\) 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 3 5 89
2670.2.a.a 2670.a 1.a $1$ $21.320$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
2670.2.a.b 2670.a 1.a $1$ $21.320$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
2670.2.a.c 2670.a 1.a $1$ $21.320$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
2670.2.a.d 2670.a 1.a $1$ $21.320$ \(\Q\) None \(1\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
2670.2.a.e 2670.a 1.a $1$ $21.320$ \(\Q\) None \(1\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
2670.2.a.f 2670.a 1.a $1$ $21.320$ \(\Q\) None \(1\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
2670.2.a.g 2670.a 1.a $2$ $21.320$ \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
2670.2.a.h 2670.a 1.a $2$ $21.320$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots\)
2670.2.a.i 2670.a 1.a $2$ $21.320$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
2670.2.a.j 2670.a 1.a $3$ $21.320$ 3.3.148.1 None \(-3\) \(-3\) \(3\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
2670.2.a.k 2670.a 1.a $3$ $21.320$ 3.3.404.1 None \(-3\) \(3\) \(-3\) \(4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2670.2.a.l 2670.a 1.a $3$ $21.320$ 3.3.148.1 None \(3\) \(-3\) \(3\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
2670.2.a.m 2670.a 1.a $3$ $21.320$ 3.3.469.1 None \(3\) \(-3\) \(3\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
2670.2.a.n 2670.a 1.a $3$ $21.320$ 3.3.148.1 None \(3\) \(3\) \(-3\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
2670.2.a.o 2670.a 1.a $4$ $21.320$ 4.4.31288.1 None \(-4\) \(-4\) \(4\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
2670.2.a.p 2670.a 1.a $4$ $21.320$ 4.4.47032.1 None \(4\) \(4\) \(-4\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2670.2.a.q 2670.a 1.a $5$ $21.320$ 5.5.2991204.1 None \(-5\) \(5\) \(5\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{2}q^{7}+\cdots\)
2670.2.a.r 2670.a 1.a $5$ $21.320$ 5.5.21712324.1 None \(5\) \(-5\) \(-5\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
2670.2.a.s 2670.a 1.a $5$ $21.320$ 5.5.15020836.1 None \(5\) \(5\) \(5\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
2670.2.a.t 2670.a 1.a $7$ $21.320$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(-7\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(534))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\)\(^{\oplus 2}\)