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Properties

Label 15.11
Level 15
Weight 11
Dimension 52
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(15))\).

Total New Old
Modular forms 88 56 32
Cusp forms 72 52 20
Eisenstein series 16 4 12

Trace form

\( 52 q - 64 q^{2} + 44 q^{3} - 1224 q^{4} + 10676 q^{5} + 8896 q^{6} - 39944 q^{7} - 39948 q^{8} + 171460 q^{9} + O(q^{10}) \) \( 52 q - 64 q^{2} + 44 q^{3} - 1224 q^{4} + 10676 q^{5} + 8896 q^{6} - 39944 q^{7} - 39948 q^{8} + 171460 q^{9} + 344524 q^{10} + 32080 q^{11} - 576380 q^{12} + 630056 q^{13} - 467956 q^{15} + 2468864 q^{16} + 347360 q^{17} - 4503592 q^{18} + 4763640 q^{19} + 24132564 q^{20} + 1701888 q^{21} - 37749400 q^{22} - 30995704 q^{23} - 12121848 q^{24} + 19687636 q^{25} + 80977840 q^{26} + 13322636 q^{27} - 115886808 q^{28} - 21240284 q^{30} + 37323864 q^{31} - 81249676 q^{32} - 101522456 q^{33} + 41699032 q^{34} + 91578920 q^{35} + 554674688 q^{36} - 180538824 q^{37} + 44187744 q^{38} - 333949936 q^{39} - 657800592 q^{40} + 149264920 q^{41} + 1467214272 q^{42} + 592983800 q^{43} - 383741684 q^{45} - 3021287288 q^{46} - 257112832 q^{47} + 647854972 q^{48} + 1993978364 q^{49} + 909704384 q^{50} + 631338256 q^{51} - 720112008 q^{52} - 152646064 q^{53} - 4481249264 q^{54} - 171284304 q^{55} + 1735516800 q^{56} + 2802185360 q^{57} + 255965768 q^{58} - 3652152344 q^{60} - 2417511896 q^{61} - 969372632 q^{62} + 462574440 q^{63} + 7423253768 q^{64} + 7250334488 q^{65} + 1315846640 q^{66} - 14538445208 q^{67} - 12869460704 q^{68} + 1383058176 q^{69} + 10163849400 q^{70} + 7511442640 q^{71} + 3099955404 q^{72} + 12126056384 q^{73} - 1299366676 q^{75} + 7697464096 q^{76} - 13264676792 q^{77} - 9657137120 q^{78} - 14729216080 q^{79} - 15692039116 q^{80} - 16436158388 q^{81} + 41493340248 q^{82} + 30753878864 q^{83} + 26957446584 q^{84} - 4963698488 q^{85} - 46532117120 q^{86} - 8686965784 q^{87} - 9160290648 q^{88} + 6225772724 q^{90} + 37463722736 q^{91} + 30045377384 q^{92} - 15624450624 q^{93} - 94908576248 q^{94} - 58265269776 q^{95} - 33272381152 q^{96} - 887505288 q^{97} + 54432471592 q^{98} + 79216068560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.11.c \(\chi_{15}(11, \cdot)\) 15.11.c.a 14 1
15.11.d \(\chi_{15}(14, \cdot)\) 15.11.d.a 1 1
15.11.d.b 1
15.11.d.c 16
15.11.f \(\chi_{15}(7, \cdot)\) 15.11.f.a 20 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)