Properties

Label 7.4.a
Level $7$
Weight $4$
Character orbit 7.a
Rep. character $\chi_{7}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(7))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

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

\(7\)Dim.
\(+\)\(1\)

Trace form

\( q - q^{2} - 2 q^{3} - 7 q^{4} + 16 q^{5} + 2 q^{6} - 7 q^{7} + 15 q^{8} - 23 q^{9} + O(q^{10}) \) \( q - q^{2} - 2 q^{3} - 7 q^{4} + 16 q^{5} + 2 q^{6} - 7 q^{7} + 15 q^{8} - 23 q^{9} - 16 q^{10} - 8 q^{11} + 14 q^{12} + 28 q^{13} + 7 q^{14} - 32 q^{15} + 41 q^{16} + 54 q^{17} + 23 q^{18} - 110 q^{19} - 112 q^{20} + 14 q^{21} + 8 q^{22} + 48 q^{23} - 30 q^{24} + 131 q^{25} - 28 q^{26} + 100 q^{27} + 49 q^{28} - 110 q^{29} + 32 q^{30} + 12 q^{31} - 161 q^{32} + 16 q^{33} - 54 q^{34} - 112 q^{35} + 161 q^{36} - 246 q^{37} + 110 q^{38} - 56 q^{39} + 240 q^{40} + 182 q^{41} - 14 q^{42} + 128 q^{43} + 56 q^{44} - 368 q^{45} - 48 q^{46} + 324 q^{47} - 82 q^{48} + 49 q^{49} - 131 q^{50} - 108 q^{51} - 196 q^{52} - 162 q^{53} - 100 q^{54} - 128 q^{55} - 105 q^{56} + 220 q^{57} + 110 q^{58} + 810 q^{59} + 224 q^{60} - 488 q^{61} - 12 q^{62} + 161 q^{63} - 167 q^{64} + 448 q^{65} - 16 q^{66} + 244 q^{67} - 378 q^{68} - 96 q^{69} + 112 q^{70} - 768 q^{71} - 345 q^{72} - 702 q^{73} + 246 q^{74} - 262 q^{75} + 770 q^{76} + 56 q^{77} + 56 q^{78} + 440 q^{79} + 656 q^{80} + 421 q^{81} - 182 q^{82} - 1302 q^{83} - 98 q^{84} + 864 q^{85} - 128 q^{86} + 220 q^{87} - 120 q^{88} + 730 q^{89} + 368 q^{90} - 196 q^{91} - 336 q^{92} - 24 q^{93} - 324 q^{94} - 1760 q^{95} + 322 q^{96} + 294 q^{97} - 49 q^{98} + 184 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
7.4.a.a 7.a 1.a $1$ $0.413$ \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)