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Properties

Label 2070.2.a
Level $2070$
Weight $2$
Character orbit 2070.a
Rep. character $\chi_{2070}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $26$
Sturm bound $864$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2070))\).

Total New Old
Modular forms 448 34 414
Cusp forms 417 34 383
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(+\)\(-\)\(-\)$+$\(2\)
\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(2\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(12\)
Minus space\(-\)\(22\)

Trace form

\( 34 q - 2 q^{2} + 34 q^{4} - 2 q^{8} + O(q^{10}) \) \( 34 q - 2 q^{2} + 34 q^{4} - 2 q^{8} - 12 q^{11} + 4 q^{13} + 8 q^{14} + 34 q^{16} + 4 q^{17} + 12 q^{19} + 20 q^{22} + 34 q^{25} + 4 q^{29} - 12 q^{31} - 2 q^{32} + 12 q^{34} - 32 q^{37} + 4 q^{38} + 8 q^{41} - 12 q^{43} - 12 q^{44} + 24 q^{47} + 46 q^{49} - 2 q^{50} + 4 q^{52} + 32 q^{53} + 8 q^{56} + 4 q^{58} + 24 q^{59} + 24 q^{61} + 34 q^{64} - 8 q^{65} + 44 q^{67} + 4 q^{68} + 4 q^{70} - 20 q^{71} + 28 q^{73} + 32 q^{74} + 12 q^{76} + 56 q^{77} + 24 q^{79} + 20 q^{82} + 20 q^{83} + 32 q^{85} - 4 q^{86} + 20 q^{88} + 20 q^{89} + 32 q^{91} - 8 q^{94} + 8 q^{95} - 4 q^{97} - 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\) 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 23
2070.2.a.a 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.b 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
2070.2.a.c 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
2070.2.a.d 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.e 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.f 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.g 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
2070.2.a.h 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{13}+\cdots\)
2070.2.a.i 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.j 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.k 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.l 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.m 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots\)
2070.2.a.n 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.o 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.p 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.q 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.r 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
2070.2.a.s 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.t 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.u 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.v 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.w 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-2\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.x 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{21}) \) None \(2\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.y 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.z 2070.a 1.a $3$ $16.529$ 3.3.1101.1 None \(-3\) \(0\) \(3\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)