Properties

Label 140.6.a
Level $140$
Weight $6$
Character orbit 140.a
Rep. character $\chi_{140}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $4$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 140.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(140))\).

Total New Old
Modular forms 126 10 116
Cusp forms 114 10 104
Eisenstein series 12 0 12

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

\(2\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(4\)
Minus space\(-\)\(6\)

Trace form

\( 10 q - 44 q^{3} + 656 q^{9} + O(q^{10}) \) \( 10 q - 44 q^{3} + 656 q^{9} + 750 q^{11} + 404 q^{13} + 550 q^{15} - 516 q^{17} + 2072 q^{19} + 490 q^{21} + 6240 q^{23} + 6250 q^{25} - 7964 q^{27} + 1706 q^{29} - 10796 q^{31} + 14492 q^{33} + 2450 q^{35} + 15968 q^{37} - 5058 q^{39} - 23284 q^{41} + 19068 q^{43} + 5800 q^{45} + 21964 q^{47} + 24010 q^{49} + 42474 q^{51} - 11804 q^{53} - 27800 q^{55} + 98460 q^{57} - 1452 q^{59} + 56576 q^{61} + 23128 q^{63} + 11950 q^{65} - 70300 q^{67} - 36844 q^{69} + 107576 q^{71} - 69176 q^{73} - 27500 q^{75} + 47432 q^{77} + 22714 q^{79} - 41518 q^{81} - 119744 q^{83} + 20050 q^{85} - 121044 q^{87} - 173352 q^{89} - 38318 q^{91} - 109756 q^{93} - 2100 q^{95} - 105644 q^{97} + 7676 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(140))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
140.6.a.a \(2\) \(22.454\) \(\Q(\sqrt{1009}) \) None \(0\) \(-23\) \(-50\) \(98\) \(-\) \(+\) \(-\) \(q+(-11-\beta )q^{3}-5^{2}q^{5}+7^{2}q^{7}+(130+\cdots)q^{9}+\cdots\)
140.6.a.b \(2\) \(22.454\) \(\Q(\sqrt{1009}) \) None \(0\) \(-17\) \(50\) \(-98\) \(-\) \(-\) \(+\) \(q+(-8-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(73+\cdots)q^{9}+\cdots\)
140.6.a.c \(3\) \(22.454\) 3.3.3101016.1 None \(0\) \(-10\) \(-75\) \(-147\) \(-\) \(+\) \(+\) \(q+(-3-\beta _{1})q^{3}-5^{2}q^{5}-7^{2}q^{7}+(-23+\cdots)q^{9}+\cdots\)
140.6.a.d \(3\) \(22.454\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(6\) \(75\) \(147\) \(-\) \(-\) \(-\) \(q+(2+\beta _{1})q^{3}+5^{2}q^{5}+7^{2}q^{7}+(94+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(140))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(140)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)