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Properties

Label 3005.2.a
Level $3005$
Weight $2$
Character orbit 3005.a
Rep. character $\chi_{3005}(1,\cdot)$
Character field $\Q$
Dimension $201$
Newform subspaces $4$
Sturm bound $602$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3005 = 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3005.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(602\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3005))\).

Total New Old
Modular forms 302 201 101
Cusp forms 299 201 98
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.

\(5\)\(601\)FrickeDim
\(+\)\(+\)$+$\(43\)
\(+\)\(-\)$-$\(57\)
\(-\)\(+\)$-$\(57\)
\(-\)\(-\)$+$\(44\)
Plus space\(+\)\(87\)
Minus space\(-\)\(114\)

Trace form

\( 201 q - q^{2} + 4 q^{3} + 203 q^{4} + q^{5} + 12 q^{6} + 4 q^{7} + 3 q^{8} + 209 q^{9} + O(q^{10}) \) \( 201 q - q^{2} + 4 q^{3} + 203 q^{4} + q^{5} + 12 q^{6} + 4 q^{7} + 3 q^{8} + 209 q^{9} + 3 q^{10} - 4 q^{11} + 28 q^{12} + 10 q^{13} + 12 q^{14} + 195 q^{16} + 6 q^{17} + 3 q^{18} + 20 q^{19} - q^{20} - 16 q^{22} - 8 q^{23} + 20 q^{24} + 201 q^{25} - 26 q^{26} + 16 q^{27} - 16 q^{28} - 2 q^{29} - 4 q^{30} + 12 q^{31} - 5 q^{32} - 8 q^{33} - 14 q^{34} + 199 q^{36} - 2 q^{37} - 40 q^{38} - 8 q^{39} + 15 q^{40} + 14 q^{41} - 32 q^{42} - 16 q^{44} + 5 q^{45} + 12 q^{46} - 16 q^{47} + 84 q^{48} + 241 q^{49} - q^{50} + 8 q^{51} + 38 q^{52} + 2 q^{53} + 28 q^{54} + 4 q^{55} - 32 q^{56} + 36 q^{57} - 22 q^{58} + 12 q^{59} - 16 q^{60} + 34 q^{61} - 24 q^{62} + 16 q^{63} + 179 q^{64} + 10 q^{65} - 28 q^{66} + 14 q^{68} - 12 q^{69} - 12 q^{70} - 32 q^{71} + 87 q^{72} + 30 q^{73} - 38 q^{74} + 4 q^{75} + 72 q^{76} - 8 q^{77} + 32 q^{78} + 4 q^{79} - 17 q^{80} + 281 q^{81} - 22 q^{82} + 4 q^{83} + 12 q^{84} + 2 q^{85} + 4 q^{86} - 36 q^{87} - 48 q^{88} - 10 q^{89} + 39 q^{90} - 16 q^{91} - 36 q^{92} + 24 q^{93} - 20 q^{95} + 60 q^{96} + 10 q^{97} - 73 q^{98} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3005))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 601
3005.2.a.a 3005.a 1.a $43$ $23.995$ None \(0\) \(-9\) \(-43\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$
3005.2.a.b 3005.a 1.a $44$ $23.995$ None \(-9\) \(-23\) \(44\) \(-30\) $-$ $-$ $\mathrm{SU}(2)$
3005.2.a.c 3005.a 1.a $57$ $23.995$ None \(-2\) \(11\) \(-57\) \(10\) $+$ $-$ $\mathrm{SU}(2)$
3005.2.a.d 3005.a 1.a $57$ $23.995$ None \(10\) \(25\) \(57\) \(32\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(601))\)\(^{\oplus 2}\)