Properties

Label 7.14
Level 7
Weight 14
Dimension 23
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(7))\).

Total New Old
Modular forms 29 27 2
Cusp forms 23 23 0
Eisenstein series 6 4 2

Trace form

\( 23 q - 3 q^{2} - 732 q^{3} - 16387 q^{4} + 47034 q^{5} - 279942 q^{6} + 375641 q^{7} - 49137 q^{8} + 2144115 q^{9} + O(q^{10}) \) \( 23 q - 3 q^{2} - 732 q^{3} - 16387 q^{4} + 47034 q^{5} - 279942 q^{6} + 375641 q^{7} - 49137 q^{8} + 2144115 q^{9} - 3412098 q^{10} + 6603396 q^{11} + 1933050 q^{12} - 28489118 q^{13} - 51732807 q^{14} + 222371112 q^{15} - 228808975 q^{16} - 187989666 q^{17} + 623979555 q^{18} + 717129484 q^{19} - 2329603584 q^{20} + 651643020 q^{21} + 921127140 q^{22} - 741101616 q^{23} - 551833566 q^{24} + 2859410201 q^{25} - 1882333404 q^{26} + 3079251912 q^{27} - 5077980859 q^{28} - 4754971182 q^{29} + 18343127094 q^{30} + 3272676256 q^{31} - 25747589553 q^{32} - 8070949704 q^{33} + 15740543646 q^{34} - 9377155242 q^{35} - 8971879335 q^{36} + 2546891554 q^{37} + 90115575672 q^{38} + 40364911440 q^{39} - 67719376080 q^{40} - 136444433706 q^{41} - 121501666314 q^{42} + 116999995060 q^{43} + 165542303556 q^{44} + 154934206650 q^{45} + 187496325630 q^{46} - 90083260560 q^{47} - 1048507061250 q^{48} - 182226639049 q^{49} + 361458218013 q^{50} + 915877635384 q^{51} + 1117861686844 q^{52} - 53497886622 q^{53} - 1248386893230 q^{54} - 651645370728 q^{55} - 1977873684465 q^{56} + 41832418752 q^{57} + 2830827074706 q^{58} + 2406993851580 q^{59} + 718098303804 q^{60} - 2028888278822 q^{61} - 4490748583704 q^{62} - 3496564250235 q^{63} + 1498258895585 q^{64} + 4780085827524 q^{65} + 9272361154374 q^{66} + 726018910948 q^{67} - 4151480070990 q^{68} - 11932165417968 q^{69} - 8497249945254 q^{70} + 5067748539816 q^{71} + 15311480453823 q^{72} + 7105467922990 q^{73} + 5070291270000 q^{74} - 11240309132652 q^{75} - 24376441034414 q^{76} - 6366309918276 q^{77} + 7312326116928 q^{78} + 12454092498040 q^{79} + 26389262427888 q^{80} + 8513196484959 q^{81} - 15528037464450 q^{82} - 19058763856356 q^{83} - 26915122244430 q^{84} + 6842311958340 q^{85} + 26480843462424 q^{86} + 25538752269120 q^{87} - 7665307122240 q^{88} - 5732241401298 q^{89} - 21195747882564 q^{90} - 13004660360258 q^{91} - 7903306557144 q^{92} + 23718439410888 q^{93} + 17597311757154 q^{94} - 17000176593408 q^{95} - 7675751295870 q^{96} + 23954043868174 q^{97} + 1361032641885 q^{98} - 9820452567852 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(7))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.14.a \(\chi_{7}(1, \cdot)\) 7.14.a.a 3 1
7.14.a.b 4
7.14.c \(\chi_{7}(2, \cdot)\) 7.14.c.a 16 2