Properties

Label 6005.2.a
Level $6005$
Weight $2$
Character orbit 6005.a
Rep. character $\chi_{6005}(1,\cdot)$
Character field $\Q$
Dimension $401$
Newform subspaces $7$
Sturm bound $1202$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6005 = 5 \cdot 1201 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6005.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(1202\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6005))\).

Total New Old
Modular forms 602 401 201
Cusp forms 599 401 198
Eisenstein series 3 0 3

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

\(5\)\(1201\)FrickeDim
\(+\)\(+\)$+$\(87\)
\(+\)\(-\)$-$\(113\)
\(-\)\(+\)$-$\(113\)
\(-\)\(-\)$+$\(88\)
Plus space\(+\)\(175\)
Minus space\(-\)\(226\)

Trace form

\( 401 q + 3 q^{2} + 4 q^{3} + 407 q^{4} + q^{5} + 8 q^{7} + 3 q^{8} + 413 q^{9} + O(q^{10}) \) \( 401 q + 3 q^{2} + 4 q^{3} + 407 q^{4} + q^{5} + 8 q^{7} + 3 q^{8} + 413 q^{9} + 3 q^{10} + 12 q^{11} - 4 q^{12} + 10 q^{13} - 12 q^{14} + 4 q^{15} + 423 q^{16} + 2 q^{17} - 9 q^{18} + 20 q^{19} - q^{20} + 4 q^{21} - 8 q^{23} - 8 q^{24} + 401 q^{25} - 2 q^{26} - 8 q^{27} + 32 q^{28} + 6 q^{29} + 12 q^{30} + 12 q^{31} - q^{32} - 8 q^{33} - 14 q^{34} + 4 q^{35} + 479 q^{36} + 10 q^{37} + 16 q^{38} + 12 q^{39} + 15 q^{40} + 10 q^{41} + 20 q^{42} + 36 q^{43} + 56 q^{44} + 5 q^{45} + 64 q^{46} + 8 q^{47} + 48 q^{48} + 421 q^{49} + 3 q^{50} - 20 q^{51} + 6 q^{52} - 22 q^{53} + 40 q^{54} - 4 q^{55} + 32 q^{56} + 8 q^{57} + 26 q^{58} - 24 q^{59} + 28 q^{60} + 18 q^{61} - 24 q^{62} - 16 q^{63} + 403 q^{64} + 2 q^{65} + 56 q^{66} + 60 q^{67} + 34 q^{68} - 56 q^{69} - 8 q^{70} - 20 q^{71} - 9 q^{72} + 38 q^{73} - 26 q^{74} + 4 q^{75} + 76 q^{76} - 60 q^{77} - 60 q^{78} + 52 q^{79} + 15 q^{80} + 417 q^{81} - 78 q^{82} - 44 q^{83} - 20 q^{84} + 10 q^{85} + 52 q^{86} - 68 q^{87} - 12 q^{88} + 6 q^{89} + 23 q^{90} + 4 q^{91} - 8 q^{92} - 52 q^{93} - 44 q^{94} + 4 q^{95} - 4 q^{96} + 34 q^{97} + 7 q^{98} + 76 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6005))\) 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 1201
6005.2.a.a 6005.a 1.a $1$ $47.950$ \(\Q\) None \(-2\) \(-2\) \(1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\)
6005.2.a.b 6005.a 1.a $1$ $47.950$ \(\Q\) None \(-1\) \(0\) \(1\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
6005.2.a.c 6005.a 1.a $4$ $47.950$ 4.4.2777.1 None \(2\) \(-2\) \(-4\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
6005.2.a.d 6005.a 1.a $83$ $47.950$ None \(1\) \(-4\) \(-83\) \(2\) $+$ $+$ $\mathrm{SU}(2)$
6005.2.a.e 6005.a 1.a $88$ $47.950$ None \(-14\) \(-34\) \(88\) \(-35\) $-$ $-$ $\mathrm{SU}(2)$
6005.2.a.f 6005.a 1.a $111$ $47.950$ None \(20\) \(40\) \(111\) \(39\) $-$ $+$ $\mathrm{SU}(2)$
6005.2.a.g 6005.a 1.a $113$ $47.950$ None \(-3\) \(6\) \(-113\) \(7\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1201))\)\(^{\oplus 2}\)