Properties

Label 6035.2.a
Level $6035$
Weight $2$
Character orbit 6035.a
Rep. character $\chi_{6035}(1,\cdot)$
Character field $\Q$
Dimension $375$
Newform subspaces $8$
Sturm bound $1296$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6035.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1296\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6035))\).

Total New Old
Modular forms 652 375 277
Cusp forms 645 375 270
Eisenstein series 7 0 7

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

\(5\)\(17\)\(71\)FrickeDim
\(+\)\(+\)\(+\)$+$\(44\)
\(+\)\(+\)\(-\)$-$\(49\)
\(+\)\(-\)\(+\)$-$\(49\)
\(+\)\(-\)\(-\)$+$\(44\)
\(-\)\(+\)\(+\)$-$\(59\)
\(-\)\(+\)\(-\)$+$\(36\)
\(-\)\(-\)\(+\)$+$\(36\)
\(-\)\(-\)\(-\)$-$\(58\)
Plus space\(+\)\(160\)
Minus space\(-\)\(215\)

Trace form

\( 375 q - 3 q^{2} + 4 q^{3} + 377 q^{4} + 3 q^{5} - 4 q^{6} + 16 q^{7} - 15 q^{8} + 379 q^{9} + O(q^{10}) \) \( 375 q - 3 q^{2} + 4 q^{3} + 377 q^{4} + 3 q^{5} - 4 q^{6} + 16 q^{7} - 15 q^{8} + 379 q^{9} + q^{10} - 4 q^{11} - 4 q^{12} + 26 q^{13} - 8 q^{14} - 4 q^{15} + 369 q^{16} - q^{17} - 39 q^{18} + 12 q^{19} + 5 q^{20} + 32 q^{21} - 36 q^{22} - 24 q^{23} - 4 q^{24} + 375 q^{25} - 2 q^{26} + 16 q^{27} + 24 q^{28} + 18 q^{29} + 28 q^{30} + 16 q^{31} - 63 q^{32} - 24 q^{33} - 3 q^{34} + 461 q^{36} + 26 q^{37} + 36 q^{38} - 3 q^{40} + 6 q^{41} + 72 q^{42} + 20 q^{43} + 60 q^{44} + 23 q^{45} - 24 q^{46} - 16 q^{47} + 100 q^{48} + 463 q^{49} - 3 q^{50} - 4 q^{51} + 14 q^{52} - 30 q^{53} + 88 q^{54} - 12 q^{55} + 64 q^{56} + 40 q^{57} - 50 q^{58} - 28 q^{59} + 28 q^{60} + 58 q^{61} + 24 q^{62} - 16 q^{63} + 305 q^{64} + 10 q^{65} + 56 q^{66} + 36 q^{67} - 7 q^{68} - 24 q^{69} - q^{71} - 107 q^{72} + 102 q^{73} - 2 q^{74} + 4 q^{75} + 44 q^{76} - 56 q^{77} - 8 q^{78} - 24 q^{79} + 29 q^{80} + 367 q^{81} + 18 q^{82} - 44 q^{83} + 80 q^{84} - q^{85} - 108 q^{86} - 104 q^{87} - 100 q^{88} + 30 q^{89} - 19 q^{90} + 64 q^{91} - 16 q^{92} - 16 q^{93} + 8 q^{94} + 12 q^{95} + 36 q^{96} + 22 q^{97} + 21 q^{98} - 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6035))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 17 71
6035.2.a.a 6035.a 1.a $36$ $48.190$ None \(-3\) \(-8\) \(36\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$
6035.2.a.b 6035.a 1.a $36$ $48.190$ None \(-1\) \(-4\) \(36\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$
6035.2.a.c 6035.a 1.a $44$ $48.190$ None \(-4\) \(-4\) \(-44\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$
6035.2.a.d 6035.a 1.a $44$ $48.190$ None \(-2\) \(-8\) \(-44\) \(-13\) $+$ $-$ $-$ $\mathrm{SU}(2)$
6035.2.a.e 6035.a 1.a $49$ $48.190$ None \(1\) \(10\) \(-49\) \(15\) $+$ $-$ $+$ $\mathrm{SU}(2)$
6035.2.a.f 6035.a 1.a $49$ $48.190$ None \(3\) \(6\) \(-49\) \(11\) $+$ $+$ $-$ $\mathrm{SU}(2)$
6035.2.a.g 6035.a 1.a $58$ $48.190$ None \(1\) \(6\) \(58\) \(13\) $-$ $-$ $-$ $\mathrm{SU}(2)$
6035.2.a.h 6035.a 1.a $59$ $48.190$ None \(2\) \(6\) \(59\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(355))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1207))\)\(^{\oplus 2}\)