Properties

Label 4140.2.a
Level $4140$
Weight $2$
Character orbit 4140.a
Rep. character $\chi_{4140}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $21$
Sturm bound $1728$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(1728\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4140))\).

Total New Old
Modular forms 888 38 850
Cusp forms 841 38 803
Eisenstein series 47 0 47

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.
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(16\)
Minus space\(-\)\(22\)

Trace form

\( 38 q - 4 q^{7} + O(q^{10}) \) \( 38 q - 4 q^{7} + 4 q^{17} + 8 q^{19} + 38 q^{25} + 10 q^{29} + 14 q^{31} - 6 q^{35} + 12 q^{37} - 10 q^{41} + 32 q^{43} - 12 q^{47} + 40 q^{49} - 4 q^{53} - 6 q^{59} - 4 q^{61} + 4 q^{65} + 4 q^{67} - 38 q^{71} + 12 q^{73} - 4 q^{77} - 28 q^{79} + 20 q^{83} - 10 q^{85} + 20 q^{89} + 12 q^{91} + 8 q^{95} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4140))\) 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
4140.2.a.a 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+2q^{13}-6q^{17}+2q^{19}+\cdots\)
4140.2.a.b 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+2q^{11}-2q^{13}+7q^{17}+\cdots\)
4140.2.a.c 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}-2q^{13}-6q^{17}+\cdots\)
4140.2.a.d 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}+q^{13}-4q^{19}+\cdots\)
4140.2.a.e 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(-5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{7}+4q^{13}+3q^{17}-4q^{19}+\cdots\)
4140.2.a.f 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+6q^{11}-q^{13}+2q^{19}+\cdots\)
4140.2.a.g 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
4140.2.a.h 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-6q^{11}+6q^{13}-7q^{17}+\cdots\)
4140.2.a.i 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{13}+3q^{17}-4q^{19}+\cdots\)
4140.2.a.j 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-6q^{13}-2q^{17}+6q^{19}+q^{23}+\cdots\)
4140.2.a.k 4140.a 1.a $1$ $33.058$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{13}-4q^{17}-4q^{19}+\cdots\)
4140.2.a.l 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-\beta )q^{13}+\cdots\)
4140.2.a.m 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-2q^{11}+(-1-\beta )q^{13}+\cdots\)
4140.2.a.n 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-2\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
4140.2.a.o 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+2\beta )q^{7}+(1+3\beta )q^{11}+(-5+\cdots)q^{13}+\cdots\)
4140.2.a.p 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{15}) \) None \(0\) \(0\) \(-2\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+(-1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
4140.2.a.q 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-\beta )q^{13}+\cdots\)
4140.2.a.r 4140.a 1.a $2$ $33.058$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+(2-\beta )q^{11}-\beta q^{13}+(1+\cdots)q^{17}+\cdots\)
4140.2.a.s 4140.a 1.a $3$ $33.058$ 3.3.3144.1 None \(0\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(1-\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
4140.2.a.t 4140.a 1.a $5$ $33.058$ 5.5.14345904.1 None \(0\) \(0\) \(-5\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta _{3})q^{7}+(-1+\beta _{4})q^{11}+\cdots\)
4140.2.a.u 4140.a 1.a $5$ $33.058$ 5.5.14345904.1 None \(0\) \(0\) \(5\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta _{3})q^{7}+(1-\beta _{4})q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2070))\)\(^{\oplus 2}\)