Properties

Label 69.7
Level 69
Weight 7
Dimension 768
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 2464
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(2464\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(69))\).

Total New Old
Modular forms 1100 808 292
Cusp forms 1012 768 244
Eisenstein series 88 40 48

Trace form

\( 768q + 43q^{3} - 150q^{4} - 11q^{6} + 550q^{7} - 1469q^{9} + O(q^{10}) \) \( 768q + 43q^{3} - 150q^{4} - 11q^{6} + 550q^{7} - 1469q^{9} - 22q^{10} + 3445q^{12} - 1034q^{13} - 10483q^{15} + 55146q^{16} + 22880q^{17} - 13387q^{18} - 10538q^{19} - 157696q^{20} - 56375q^{21} - 44q^{22} + 65824q^{23} + 179498q^{24} + 108120q^{25} + 109120q^{26} + 57835q^{27} - 166166q^{28} - 117040q^{29} - 311179q^{30} - 189386q^{31} + 119680q^{32} + 234245q^{33} - 800074q^{34} + 143000q^{35} + 147247q^{36} + 1071766q^{37} + 550550q^{38} - 36839q^{39} - 1254022q^{40} - 470800q^{41} - 1274141q^{42} - 1080794q^{43} - 867482q^{44} - 22q^{45} + 1085018q^{46} + 1036816q^{47} + 1611837q^{48} + 2354228q^{49} + 2406250q^{50} + 463309q^{51} + 429550q^{52} - 367840q^{53} + 1053987q^{54} - 2574022q^{55} - 3696550q^{56} - 2973311q^{57} - 793672q^{58} + 1603448q^{59} + 2041919q^{60} + 841654q^{61} + 2130777q^{63} - 524310q^{64} + 2108898q^{66} - 345770q^{67} - 770451q^{69} - 44q^{70} - 5913611q^{72} - 1276154q^{73} - 5387470q^{74} - 5572869q^{75} + 2092024q^{76} + 5131280q^{77} + 10404119q^{78} + 6792742q^{79} + 10626462q^{80} + 6248411q^{81} - 196042q^{82} - 2474560q^{83} - 9374145q^{84} - 14164942q^{85} - 15634300q^{86} - 9184571q^{87} - 10726694q^{88} - 5901720q^{89} - 5002976q^{90} + 289388q^{91} + 4954950q^{92} + 8366606q^{93} + 13785156q^{94} + 6510416q^{95} + 12967482q^{96} + 12863278q^{97} + 23243792q^{98} + 11605429q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(69))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
69.7.b \(\chi_{69}(47, \cdot)\) 69.7.b.a 44 1
69.7.d \(\chi_{69}(22, \cdot)\) 69.7.d.a 24 1
69.7.f \(\chi_{69}(7, \cdot)\) 69.7.f.a 240 10
69.7.h \(\chi_{69}(2, \cdot)\) 69.7.h.a 460 10

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

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