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Properties

Label 207.7
Level 207
Weight 7
Dimension 7401
Nonzero newspaces 8
Sturm bound 22176
Trace bound 2

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Defining parameters

Level: \( N \) = \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(22176\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(207))\).

Total New Old
Modular forms 9680 7591 2089
Cusp forms 9328 7401 1927
Eisenstein series 352 190 162

Trace form

\( 7401 q - 27 q^{2} - 92 q^{3} + 105 q^{4} + 405 q^{5} - 710 q^{6} - 1887 q^{7} - 33 q^{8} + 3916 q^{9} + O(q^{10}) \) \( 7401 q - 27 q^{2} - 92 q^{3} + 105 q^{4} + 405 q^{5} - 710 q^{6} - 1887 q^{7} - 33 q^{8} + 3916 q^{9} + 3405 q^{10} - 999 q^{11} + 3616 q^{12} + 273 q^{13} - 24381 q^{14} - 15974 q^{15} - 24687 q^{16} - 11473 q^{17} + 15724 q^{18} + 12669 q^{19} + 205187 q^{20} + 51646 q^{21} - 51028 q^{22} - 86510 q^{23} - 223126 q^{24} - 132933 q^{25} - 54593 q^{26} + 202024 q^{27} + 352005 q^{28} + 219845 q^{29} + 75520 q^{30} + 150825 q^{31} - 496463 q^{32} - 460034 q^{33} + 21615 q^{34} - 71533 q^{35} + 549910 q^{36} - 375987 q^{37} + 468446 q^{38} + 225454 q^{39} + 408507 q^{40} - 229135 q^{41} - 541124 q^{42} + 979317 q^{43} + 431596 q^{44} - 127646 q^{45} - 508683 q^{46} - 232700 q^{47} + 286522 q^{48} - 1941489 q^{49} - 1840076 q^{50} - 114200 q^{51} - 486195 q^{52} + 183887 q^{53} - 3001794 q^{54} + 1515297 q^{55} + 6181262 q^{56} + 2325328 q^{57} + 6439380 q^{58} + 3697421 q^{59} + 2839400 q^{60} - 2371767 q^{61} - 4633233 q^{62} - 4480554 q^{63} - 11436855 q^{64} - 10502379 q^{65} - 7455072 q^{66} - 323907 q^{67} + 3387516 q^{68} + 2392551 q^{69} + 9485958 q^{70} + 6260727 q^{71} + 8887342 q^{72} + 2437773 q^{73} + 12699050 q^{74} + 6447932 q^{75} + 1544886 q^{76} + 941093 q^{77} + 3072364 q^{78} - 9042855 q^{79} - 29643504 q^{80} - 10998868 q^{81} - 11899797 q^{82} - 9840307 q^{83} - 1634480 q^{84} + 15426867 q^{85} + 22667123 q^{86} + 1231138 q^{87} + 7561025 q^{88} + 2950827 q^{89} - 170040 q^{90} - 297556 q^{91} - 1503720 q^{92} + 5909018 q^{93} - 1945334 q^{94} + 1870667 q^{95} + 2134292 q^{96} - 6898623 q^{97} - 11621929 q^{98} + 865090 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(207))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
207.7.b \(\chi_{207}(116, \cdot)\) 207.7.b.a 44 1
207.7.d \(\chi_{207}(91, \cdot)\) 207.7.d.a 1 1
207.7.d.b 2
207.7.d.c 8
207.7.d.d 24
207.7.d.e 24
207.7.f \(\chi_{207}(22, \cdot)\) n/a 284 2
207.7.h \(\chi_{207}(47, \cdot)\) n/a 264 2
207.7.j \(\chi_{207}(10, \cdot)\) n/a 590 10
207.7.l \(\chi_{207}(8, \cdot)\) n/a 480 10
207.7.n \(\chi_{207}(2, \cdot)\) n/a 2840 20
207.7.p \(\chi_{207}(7, \cdot)\) n/a 2840 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(207)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)