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Properties

Label 48.12
Level 48
Weight 12
Dimension 293
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 1536
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(1536\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(48))\).

Total New Old
Modular forms 732 301 431
Cusp forms 676 293 383
Eisenstein series 56 8 48

Trace form

\( 293 q - 245 q^{3} - 6168 q^{4} + 2642 q^{5} - 30356 q^{6} + 84952 q^{7} - 149676 q^{8} + 338673 q^{9} + O(q^{10}) \) \( 293 q - 245 q^{3} - 6168 q^{4} + 2642 q^{5} - 30356 q^{6} + 84952 q^{7} - 149676 q^{8} + 338673 q^{9} + 1977888 q^{10} + 1622532 q^{11} - 2300264 q^{12} - 1789918 q^{13} + 3668100 q^{14} + 7593750 q^{15} - 4037424 q^{16} + 2639734 q^{17} - 13213520 q^{18} + 1202144 q^{19} - 59950000 q^{20} + 37343836 q^{21} + 122043960 q^{22} - 8398712 q^{23} - 44344212 q^{24} - 76630581 q^{25} - 217620020 q^{26} + 52468687 q^{27} + 342081920 q^{28} + 17806090 q^{29} - 491166020 q^{30} - 612319504 q^{31} + 42419520 q^{32} - 181511536 q^{33} + 1163024776 q^{34} + 796101240 q^{35} + 646116368 q^{36} + 259317002 q^{37} - 407141464 q^{38} - 186410302 q^{39} + 4845455176 q^{40} + 192769710 q^{41} - 4347244884 q^{42} - 3736130864 q^{43} - 694011848 q^{44} - 3045495066 q^{45} + 6614104256 q^{46} + 5712040512 q^{47} + 10366057632 q^{48} + 9203397993 q^{49} - 24732456732 q^{50} + 5173134810 q^{51} + 18365220144 q^{52} + 6243424546 q^{53} + 15934288820 q^{54} + 1932573408 q^{55} + 1023253056 q^{56} - 5831445720 q^{57} + 6956613576 q^{58} + 1779994316 q^{59} + 5306441816 q^{60} - 20322897662 q^{61} - 4088720580 q^{62} - 2922689304 q^{63} - 42164076096 q^{64} + 4504394748 q^{65} + 64529708524 q^{66} - 34436263680 q^{67} + 5189339872 q^{68} + 32210830492 q^{69} - 73499262952 q^{70} + 49688209016 q^{71} - 44911247324 q^{72} - 29758467366 q^{73} + 15836009516 q^{74} - 59799186919 q^{75} + 277229809776 q^{76} + 104413753328 q^{77} - 14631521160 q^{78} + 127335859792 q^{79} - 194098578488 q^{80} - 321975289723 q^{81} - 220165365288 q^{82} - 269674129620 q^{83} + 333999750616 q^{84} + 132577134932 q^{85} + 381418383568 q^{86} + 66998900730 q^{87} - 182139245760 q^{88} - 112522837170 q^{89} - 441449454280 q^{90} + 1385172288 q^{91} + 260487196336 q^{92} - 44799857528 q^{93} - 23197524920 q^{94} - 207921399736 q^{95} + 239143958152 q^{96} + 154783822746 q^{97} + 162117572008 q^{98} - 156304836400 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.12.a \(\chi_{48}(1, \cdot)\) 48.12.a.a 1 1
48.12.a.b 1
48.12.a.c 1
48.12.a.d 1
48.12.a.e 1
48.12.a.f 1
48.12.a.g 1
48.12.a.h 1
48.12.a.i 1
48.12.a.j 2
48.12.c \(\chi_{48}(47, \cdot)\) 48.12.c.a 2 1
48.12.c.b 8
48.12.c.c 12
48.12.d \(\chi_{48}(25, \cdot)\) None 0 1
48.12.f \(\chi_{48}(23, \cdot)\) None 0 1
48.12.j \(\chi_{48}(13, \cdot)\) 48.12.j.a 88 2
48.12.k \(\chi_{48}(11, \cdot)\) 48.12.k.a 172 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)