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Properties

Label 207.7.p
Level $207$
Weight $7$
Character orbit 207.p
Rep. character $\chi_{207}(7,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $2840$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 207.p (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(207, [\chi])\).

Total New Old
Modular forms 2920 2920 0
Cusp forms 2840 2840 0
Eisenstein series 80 80 0

Trace form

\( 2840 q - 9 q^{2} + 14 q^{3} + 4471 q^{4} - 11 q^{5} + 47 q^{6} - 11 q^{7} - 22 q^{8} - 1570 q^{9} + O(q^{10}) \) \( 2840 q - 9 q^{2} + 14 q^{3} + 4471 q^{4} - 11 q^{5} + 47 q^{6} - 11 q^{7} - 22 q^{8} - 1570 q^{9} - 44 q^{10} - 11 q^{11} + 6782 q^{12} - 9 q^{13} - 11 q^{14} + 20922 q^{15} + 139383 q^{16} - 44 q^{17} - 25545 q^{18} - 44 q^{19} - 11 q^{20} - 40942 q^{21} - 15274 q^{23} - 353348 q^{24} - 429415 q^{25} - 22792 q^{26} - 107530 q^{27} - 44 q^{28} + 53775 q^{29} - 311190 q^{30} + 12231 q^{31} - 713 q^{32} - 468534 q^{33} - 11 q^{34} + 62464 q^{35} + 496391 q^{36} - 44 q^{37} - 11 q^{38} + 176180 q^{39} - 470261 q^{40} - 9945 q^{41} - 22 q^{42} - 11 q^{43} - 1452 q^{44} - 112812 q^{46} - 165116 q^{47} - 217712 q^{48} - 3118687 q^{49} - 536577 q^{50} - 22 q^{51} + 54880 q^{52} - 44 q^{53} - 1355532 q^{54} - 320864 q^{55} - 1672715 q^{56} + 1161578 q^{57} - 221530 q^{58} + 1153647 q^{59} + 408298 q^{60} - 11 q^{61} - 1955362 q^{62} - 1713822 q^{63} - 9203422 q^{64} + 2406085 q^{65} - 2124969 q^{66} - 11 q^{67} + 1712955 q^{69} - 568690 q^{70} + 3795084 q^{71} + 5515544 q^{72} - 36 q^{73} - 3731915 q^{74} - 1410058 q^{75} - 11 q^{76} + 1418251 q^{77} + 12191715 q^{78} - 11 q^{79} - 16220204 q^{80} - 6332378 q^{81} - 965542 q^{82} + 1686949 q^{83} - 6932684 q^{84} - 31259 q^{85} + 12440725 q^{86} - 9111628 q^{87} - 90123 q^{88} - 44 q^{89} + 10006612 q^{90} + 107629 q^{92} + 8729158 q^{93} - 2464128 q^{94} - 5713571 q^{95} + 18723602 q^{96} - 215435 q^{97} - 4002588 q^{98} - 17223382 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.