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Properties

Label 2142.2.a
Level $2142$
Weight $2$
Character orbit 2142.a
Rep. character $\chi_{2142}(1,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $29$
Sturm bound $864$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2142.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(864\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2142))\).

Total New Old
Modular forms 448 40 408
Cusp forms 417 40 377
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.

\(2\)\(3\)\(7\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(-\)\(+\)\(+\)$-$\(3\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(3\)
\(+\)\(-\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(3\)
\(-\)\(-\)\(+\)\(+\)$+$\(3\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(14\)
Minus space\(-\)\(26\)

Trace form

\( 40 q + 40 q^{4} - 8 q^{5} + O(q^{10}) \) \( 40 q + 40 q^{4} - 8 q^{5} - 4 q^{11} - 8 q^{13} - 4 q^{14} + 40 q^{16} - 8 q^{19} - 8 q^{20} + 4 q^{22} + 64 q^{25} + 8 q^{26} - 28 q^{29} + 32 q^{31} + 8 q^{35} + 28 q^{37} - 8 q^{38} + 16 q^{41} + 8 q^{43} - 4 q^{44} + 16 q^{46} + 40 q^{49} + 8 q^{50} - 8 q^{52} + 40 q^{53} + 48 q^{55} - 4 q^{56} - 4 q^{58} + 40 q^{59} + 8 q^{61} + 32 q^{62} + 40 q^{64} + 8 q^{67} + 8 q^{71} - 44 q^{74} - 8 q^{76} - 8 q^{79} - 8 q^{80} - 16 q^{82} - 40 q^{83} - 4 q^{85} + 24 q^{86} + 4 q^{88} - 48 q^{89} + 4 q^{91} + 40 q^{95} + 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2142))\) 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 7 17
2142.2.a.a 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
2142.2.a.b 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
2142.2.a.c 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
2142.2.a.d 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-2q^{13}+\cdots\)
2142.2.a.e 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
2142.2.a.f 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2142.2.a.g 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2142.2.a.h 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2142.2.a.i 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
2142.2.a.j 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
2142.2.a.k 2142.a 1.a $1$ $17.104$ \(\Q\) None \(-1\) \(0\) \(4\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots\)
2142.2.a.l 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-4\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
2142.2.a.m 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-3\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
2142.2.a.n 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
2142.2.a.o 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2142.2.a.p 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2142.2.a.q 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2142.2.a.r 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2142.2.a.s 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
2142.2.a.t 2142.a 1.a $1$ $17.104$ \(\Q\) None \(1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2142.2.a.u 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(-4\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
2142.2.a.v 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(-4\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
2142.2.a.w 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-3\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2142.2.a.x 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2142.2.a.y 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{41}) \) None \(2\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta q^{5}-q^{7}+q^{8}-\beta q^{10}+\cdots\)
2142.2.a.z 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2142.2.a.ba 2142.a 1.a $2$ $17.104$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(4\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2142.2.a.bb 2142.a 1.a $3$ $17.104$ 3.3.1016.1 None \(-3\) \(0\) \(-1\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
2142.2.a.bc 2142.a 1.a $3$ $17.104$ 3.3.1016.1 None \(3\) \(0\) \(1\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{5}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2142))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2142)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1071))\)\(^{\oplus 2}\)