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Properties

Label 48.10
Level 48
Weight 10
Dimension 239
Nonzero newspaces 4
Newform subspaces 13
Sturm bound 1280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 13 \)
Sturm bound: \(1280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(48))\).

Total New Old
Modular forms 604 247 357
Cusp forms 548 239 309
Eisenstein series 56 8 48

Trace form

\( 239 q + 79 q^{3} - 344 q^{4} + 718 q^{5} + 2188 q^{6} - 3784 q^{7} + 1428 q^{8} + 100659 q^{9} + O(q^{10}) \) \( 239 q + 79 q^{3} - 344 q^{4} + 718 q^{5} + 2188 q^{6} - 3784 q^{7} + 1428 q^{8} + 100659 q^{9} - 9376 q^{10} - 197580 q^{11} - 217160 q^{12} + 183462 q^{13} + 269124 q^{14} - 506250 q^{15} + 566096 q^{16} - 101998 q^{17} + 616336 q^{18} + 1649072 q^{19} + 1810000 q^{20} - 990620 q^{21} + 3305784 q^{22} - 1020280 q^{23} + 4600428 q^{24} - 3417295 q^{25} - 1052980 q^{26} - 5793605 q^{27} - 11944320 q^{28} + 1696838 q^{29} + 34132060 q^{30} + 11498832 q^{31} - 10940160 q^{32} - 15661480 q^{33} + 12102792 q^{34} + 3398424 q^{35} - 9247600 q^{36} - 12667890 q^{37} - 10145048 q^{38} + 72608402 q^{39} - 29204024 q^{40} - 5524470 q^{41} + 17637996 q^{42} + 36455232 q^{43} + 266951288 q^{44} - 8842302 q^{45} - 143997184 q^{46} - 110606976 q^{47} - 228141024 q^{48} + 164316619 q^{49} + 127557732 q^{50} - 121733694 q^{51} + 305761136 q^{52} + 169873118 q^{53} - 103316428 q^{54} - 166367200 q^{55} - 329081088 q^{56} - 103230408 q^{57} - 613357496 q^{58} - 107327396 q^{59} + 868477976 q^{60} + 627135078 q^{61} + 617679996 q^{62} + 101249352 q^{63} - 100459712 q^{64} - 294809964 q^{65} - 1325667188 q^{66} - 648849328 q^{67} + 485197472 q^{68} - 157363940 q^{69} + 770586648 q^{70} - 139971464 q^{71} - 86425628 q^{72} + 766424782 q^{73} - 259094804 q^{74} + 963901949 q^{75} - 1988216912 q^{76} - 849892976 q^{77} - 1090274472 q^{78} - 2380580816 q^{79} + 3633471368 q^{80} - 2369687521 q^{81} + 3541005976 q^{82} - 336747492 q^{83} - 2218757480 q^{84} - 993569236 q^{85} - 2167679536 q^{86} + 2905108746 q^{87} - 4313399488 q^{88} - 304312182 q^{89} + 2281975352 q^{90} - 4240880576 q^{91} + 5399572784 q^{92} + 596694352 q^{93} + 781671368 q^{94} + 7039361224 q^{95} - 1286807672 q^{96} + 1015179790 q^{97} + 5090745896 q^{98} - 1292750848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(48))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
48.10.a \(\chi_{48}(1, \cdot)\) 48.10.a.a 1 1
48.10.a.b 1
48.10.a.c 1
48.10.a.d 1
48.10.a.e 1
48.10.a.f 1
48.10.a.g 1
48.10.a.h 2
48.10.c \(\chi_{48}(47, \cdot)\) 48.10.c.a 2 1
48.10.c.b 4
48.10.c.c 12
48.10.d \(\chi_{48}(25, \cdot)\) None 0 1
48.10.f \(\chi_{48}(23, \cdot)\) None 0 1
48.10.j \(\chi_{48}(13, \cdot)\) 48.10.j.a 72 2
48.10.k \(\chi_{48}(11, \cdot)\) 48.10.k.a 140 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)