Properties

Label 49.6.g
Level $49$
Weight $6$
Character orbit 49.g
Rep. character $\chi_{49}(2,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $264$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(49, [\chi])\).

Total New Old
Modular forms 288 288 0
Cusp forms 264 264 0
Eisenstein series 24 24 0

Trace form

\( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} + O(q^{10}) \) \( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17} - 1336 q^{18} + 9741 q^{19} + 8330 q^{20} + 1512 q^{21} + 842 q^{22} - 1553 q^{23} + 1756 q^{24} + 13144 q^{25} - 1946 q^{26} - 19849 q^{27} - 31584 q^{28} - 30356 q^{29} + 6129 q^{30} + 43903 q^{31} + 27725 q^{32} - 3412 q^{33} - 73182 q^{34} - 17360 q^{35} - 102868 q^{36} - 22105 q^{37} + 19116 q^{38} + 109165 q^{39} + 77354 q^{40} + 47446 q^{41} + 157738 q^{42} + 6674 q^{43} + 15154 q^{44} - 130923 q^{45} - 136952 q^{46} - 195163 q^{47} - 151484 q^{48} - 131194 q^{49} + 263000 q^{50} - 84276 q^{51} - 58758 q^{52} - 110577 q^{53} + 170313 q^{54} + 290245 q^{55} + 79688 q^{56} + 47310 q^{57} + 252156 q^{58} + 127308 q^{59} + 86254 q^{60} + 166863 q^{61} - 63578 q^{62} - 243033 q^{63} - 293812 q^{64} - 16702 q^{65} - 661788 q^{66} + 46195 q^{67} + 393869 q^{68} + 321394 q^{69} - 64330 q^{70} - 61793 q^{71} + 333944 q^{72} + 21699 q^{73} + 133514 q^{74} - 431136 q^{75} + 3087 q^{76} - 48993 q^{77} - 450576 q^{78} - 181 q^{79} + 264228 q^{80} + 142090 q^{81} - 512442 q^{82} + 102424 q^{83} + 344932 q^{84} - 205502 q^{85} + 611991 q^{86} + 1427200 q^{87} + 685993 q^{88} + 145800 q^{89} + 677844 q^{90} + 732956 q^{91} + 10018 q^{92} - 1233536 q^{93} - 601938 q^{94} - 945265 q^{95} - 2372958 q^{96} - 1932952 q^{97} - 672973 q^{98} + 1090736 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.6.g.a 49.g 49.g $264$ $7.859$ None \(-13\) \(-22\) \(-52\) \(154\) $\mathrm{SU}(2)[C_{21}]$