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Properties

Label 3.11
Level 3
Weight 11
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(3))\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9} + O(q^{10}) \) \( 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9} + 152640 q^{10} - 16416 q^{12} - 339308 q^{13} + 1373760 q^{15} - 1289728 q^{16} + 699840 q^{18} - 1898924 q^{19} - 930636 q^{21} + 10025280 q^{22} - 17210880 q^{24} + 3351410 q^{25} + 9408474 q^{27} + 10478272 q^{28} - 4121280 q^{30} - 59586236 q^{31} + 90227520 q^{33} + 18420480 q^{34} - 35015328 q^{36} - 121623692 q^{37} + 9161316 q^{39} + 202705920 q^{40} - 223352640 q^{42} + 214839412 q^{43} - 74183040 q^{45} - 142623360 q^{46} + 34822656 q^{48} + 29071014 q^{49} + 165784320 q^{51} - 103149632 q^{52} + 727483680 q^{54} - 1062679680 q^{55} + 51270948 q^{57} - 170775360 q^{58} + 417623040 q^{60} + 2061587284 q^{61} - 1985046588 q^{63} - 2350292992 q^{64} - 270682560 q^{66} + 3753484948 q^{67} - 1283610240 q^{69} + 2630597760 q^{70} + 929387520 q^{72} - 5693056988 q^{73} - 90488070 q^{75} - 577272896 q^{76} + 2198715840 q^{78} + 2977295236 q^{79} + 6293324322 q^{81} - 9749335680 q^{82} - 282913344 q^{84} - 1952570880 q^{85} - 1536978240 q^{87} + 13313571840 q^{88} - 8790690240 q^{90} - 5847634072 q^{91} + 1608828372 q^{93} + 14382155520 q^{94} - 9266503680 q^{96} - 3185897852 q^{97} - 4872286080 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.11.b \(\chi_{3}(2, \cdot)\) 3.11.b.a 2 1