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Properties

Label 3007.2.a
Level $3007$
Weight $2$
Character orbit 3007.a
Rep. character $\chi_{3007}(1,\cdot)$
Character field $\Q$
Dimension $241$
Newform subspaces $4$
Sturm bound $522$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3007 = 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3007.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(522\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3007))\).

Total New Old
Modular forms 262 241 21
Cusp forms 259 241 18
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.

\(31\)\(97\)FrickeDim
\(+\)\(+\)$+$\(56\)
\(+\)\(-\)$-$\(64\)
\(-\)\(+\)$-$\(66\)
\(-\)\(-\)$+$\(55\)
Plus space\(+\)\(111\)
Minus space\(-\)\(130\)

Trace form

\( 241 q - q^{2} + 4 q^{3} + 243 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{8} + 245 q^{9} + O(q^{10}) \) \( 241 q - q^{2} + 4 q^{3} + 243 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{8} + 245 q^{9} - 2 q^{10} - 8 q^{11} + 12 q^{12} + 6 q^{13} - 4 q^{14} - 12 q^{15} + 227 q^{16} - 2 q^{17} - 25 q^{18} - 8 q^{19} - 14 q^{20} - 12 q^{21} - 28 q^{22} - 20 q^{23} - 16 q^{24} + 259 q^{25} + 34 q^{26} + 16 q^{27} - 44 q^{28} - 26 q^{29} - 28 q^{30} + q^{31} + 35 q^{32} + 8 q^{33} - 2 q^{34} - 12 q^{35} + 247 q^{36} + 18 q^{37} - 20 q^{38} - 40 q^{39} - 2 q^{40} - 14 q^{41} - 24 q^{42} - 24 q^{43} - 4 q^{44} - 50 q^{45} - 8 q^{46} - 4 q^{47} - 8 q^{48} + 221 q^{49} + 17 q^{50} + 48 q^{51} + 26 q^{52} - 2 q^{53} + 64 q^{54} - 48 q^{55} - 28 q^{56} - 24 q^{57} - 14 q^{58} - 12 q^{59} - 36 q^{60} + 26 q^{61} + 3 q^{62} - 44 q^{63} + 179 q^{64} - 8 q^{65} + 56 q^{66} - 20 q^{67} + 46 q^{68} + 20 q^{69} + 8 q^{70} + 31 q^{72} + 6 q^{73} + 22 q^{74} - 32 q^{75} + 48 q^{76} - 4 q^{77} - 76 q^{78} + 16 q^{79} - 54 q^{80} + 225 q^{81} + 46 q^{82} + 12 q^{83} - 12 q^{84} + 8 q^{85} + 8 q^{86} - 44 q^{87} - 112 q^{88} - 30 q^{89} - 62 q^{90} - 144 q^{92} + 4 q^{93} - 56 q^{94} + 32 q^{95} + 16 q^{96} - 3 q^{97} + 39 q^{98} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3007))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 31 97
3007.2.a.a 3007.a 1.a $55$ $24.011$ None \(-15\) \(-8\) \(-21\) \(-17\) $-$ $-$ $\mathrm{SU}(2)$
3007.2.a.b 3007.a 1.a $56$ $24.011$ None \(-8\) \(-12\) \(-9\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$
3007.2.a.c 3007.a 1.a $64$ $24.011$ None \(6\) \(12\) \(13\) \(3\) $+$ $-$ $\mathrm{SU}(2)$
3007.2.a.d 3007.a 1.a $66$ $24.011$ None \(16\) \(12\) \(15\) \(17\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(97))\)\(^{\oplus 2}\)