Properties

Label 14.12
Level 14
Weight 12
Dimension 22
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(14))\).

Total New Old
Modular forms 72 22 50
Cusp forms 60 22 38
Eisenstein series 12 0 12

Trace form

\( 22 q - 486 q^{3} - 2048 q^{4} + 15186 q^{5} - 46656 q^{6} + 68104 q^{7} - 390558 q^{9} + O(q^{10}) \) \( 22 q - 486 q^{3} - 2048 q^{4} + 15186 q^{5} - 46656 q^{6} + 68104 q^{7} - 390558 q^{9} - 245184 q^{10} + 2457060 q^{11} - 497664 q^{12} + 591230 q^{13} + 3729984 q^{14} + 7480968 q^{15} - 2097152 q^{16} + 8491944 q^{17} + 20198784 q^{18} - 12947098 q^{19} - 19200000 q^{20} - 58075194 q^{21} + 45078144 q^{22} + 113427624 q^{23} + 4521984 q^{24} - 231087650 q^{25} - 40719936 q^{26} + 75264156 q^{27} - 65282048 q^{28} - 105720120 q^{29} - 90244992 q^{30} + 496694996 q^{31} - 565250088 q^{33} - 545225088 q^{34} - 1430283750 q^{35} + 1527343104 q^{36} + 744915872 q^{37} + 1337082048 q^{38} + 2420822136 q^{39} - 251068416 q^{40} - 6090899760 q^{41} - 2501097408 q^{42} + 3064284116 q^{43} + 2516029440 q^{44} + 13053905202 q^{45} - 1938731136 q^{46} - 4893807348 q^{47} - 509607936 q^{48} - 14146151690 q^{49} - 1131447936 q^{50} + 20714441508 q^{51} + 3081820160 q^{52} - 1137524340 q^{53} - 9058717440 q^{54} - 31637889288 q^{55} - 3897360384 q^{56} + 5855275044 q^{57} + 16191398016 q^{58} + 21363358110 q^{59} + 4934025216 q^{60} - 26861288566 q^{61} - 42826630272 q^{62} - 19870263300 q^{63} + 23622320128 q^{64} + 50251750164 q^{65} + 8196298752 q^{66} + 18128698208 q^{67} + 8695750656 q^{68} - 45997267248 q^{69} - 11664695616 q^{70} + 11420507736 q^{71} + 20683554816 q^{72} + 77039951756 q^{73} - 4965307776 q^{74} + 776996574 q^{75} + 30729893888 q^{76} + 5462907996 q^{77} - 86764972032 q^{78} - 90454974808 q^{79} + 15923675136 q^{80} + 11588815578 q^{81} + 8393560704 q^{82} + 129680135670 q^{83} + 39467071488 q^{84} - 15485470380 q^{85} - 5974387584 q^{86} - 377918246484 q^{87} - 23353098240 q^{88} + 171490559604 q^{89} + 224543131968 q^{90} + 167978373062 q^{91} - 73887178752 q^{92} - 458471993040 q^{93} - 150177557760 q^{94} - 86426478168 q^{95} + 4630511616 q^{96} + 367531905752 q^{97} + 347442899712 q^{98} + 129769477356 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
14.12.a \(\chi_{14}(1, \cdot)\) 14.12.a.a 1 1
14.12.a.b 1
14.12.a.c 2
14.12.a.d 2
14.12.c \(\chi_{14}(9, \cdot)\) 14.12.c.a 8 2
14.12.c.b 8

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)