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Properties

Label 41.12
Level 41
Weight 12
Dimension 748
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 1680
Trace bound 2

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Defining parameters

Level: \( N \) = \( 41 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(1680\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(41))\).

Total New Old
Modular forms 790 786 4
Cusp forms 750 748 2
Eisenstein series 40 38 2

Trace form

\( 748 q + 28 q^{2} - 524 q^{3} + 2924 q^{4} - 9680 q^{5} + 12076 q^{6} + 33468 q^{7} - 168980 q^{8} + 227266 q^{9} + O(q^{10}) \) \( 748 q + 28 q^{2} - 524 q^{3} + 2924 q^{4} - 9680 q^{5} + 12076 q^{6} + 33468 q^{7} - 168980 q^{8} + 227266 q^{9} + 231820 q^{10} - 1069244 q^{11} + 741868 q^{12} + 1155456 q^{13} - 803732 q^{14} - 2434340 q^{15} - 1974292 q^{16} + 13811848 q^{17} - 5454884 q^{18} - 21322860 q^{19} + 14219500 q^{20} + 8438956 q^{21} + 25661356 q^{22} - 37286564 q^{23} - 42577940 q^{24} + 50998430 q^{25} - 27731444 q^{26} + 146558140 q^{27} - 49294356 q^{28} - 256813280 q^{29} + 2430423660 q^{30} - 477438664 q^{31} - 1955397652 q^{32} + 1516551112 q^{33} + 2167431948 q^{34} + 362622020 q^{35} - 7762189972 q^{36} - 3588660612 q^{37} - 194083540 q^{38} + 4895700812 q^{39} + 11471923160 q^{40} + 1208585958 q^{41} - 3016390184 q^{42} - 2453530144 q^{43} - 18647357972 q^{44} - 6689958640 q^{45} + 3851591276 q^{46} + 9430597168 q^{47} + 38111051756 q^{48} + 5940896834 q^{49} - 16848962820 q^{50} - 28003935824 q^{51} - 10519149332 q^{52} + 20099444436 q^{53} + 11972489580 q^{54} - 5164351940 q^{55} + 2829066220 q^{56} - 5373355700 q^{57} + 6163518220 q^{58} + 10378407460 q^{59} + 3583319020 q^{60} - 13912957344 q^{61} - 2536472084 q^{62} - 3805676804 q^{63} - 5398593556 q^{64} - 86045868850 q^{65} + 249223802812 q^{66} + 75569785368 q^{67} - 220183841416 q^{68} - 163999749188 q^{69} - 20230683180 q^{70} + 117021657516 q^{71} + 426316813720 q^{72} + 110200090376 q^{73} - 38762025212 q^{74} - 283418150780 q^{75} - 761293404240 q^{76} - 164099096004 q^{77} - 183816940268 q^{78} + 4178348540 q^{79} + 526492529060 q^{80} + 589422971408 q^{81} + 738993163468 q^{82} + 170637177136 q^{83} - 251931197892 q^{84} - 505860783450 q^{85} - 968418573804 q^{86} - 441980292980 q^{87} - 642250262940 q^{88} + 101208126120 q^{89} + 1306524749560 q^{90} + 1126209501996 q^{91} + 930696507988 q^{92} + 346903671292 q^{93} - 274467777392 q^{94} - 831281910900 q^{95} - 2400865552604 q^{96} - 782712441352 q^{97} + 544567101344 q^{98} + 1447812954952 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(41))\)

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
41.12.a \(\chi_{41}(1, \cdot)\) 41.12.a.a 16 1
41.12.a.b 20
41.12.b \(\chi_{41}(40, \cdot)\) 41.12.b.a 38 1
41.12.c \(\chi_{41}(9, \cdot)\) 41.12.c.a 74 2
41.12.d \(\chi_{41}(10, \cdot)\) 41.12.d.a 152 4
41.12.f \(\chi_{41}(4, \cdot)\) 41.12.f.a 152 4
41.12.g \(\chi_{41}(2, \cdot)\) 41.12.g.a 296 8

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(41))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(41)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)