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Properties

Label 344.2
Level 344
Weight 2
Dimension 1995
Nonzero newspaces 12
Newform subspaces 25
Sturm bound 14784
Trace bound 10

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Defining parameters

Level: \( N \) = \( 344 = 2^{3} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 25 \)
Sturm bound: \(14784\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(344))\).

Total New Old
Modular forms 3948 2159 1789
Cusp forms 3445 1995 1450
Eisenstein series 503 164 339

Trace form

\( 1995 q - 42 q^{2} - 42 q^{3} - 42 q^{4} - 42 q^{6} - 42 q^{7} - 42 q^{8} - 84 q^{9} + O(q^{10}) \) \( 1995 q - 42 q^{2} - 42 q^{3} - 42 q^{4} - 42 q^{6} - 42 q^{7} - 42 q^{8} - 84 q^{9} - 42 q^{10} - 42 q^{11} - 42 q^{12} - 42 q^{14} - 42 q^{15} - 42 q^{16} - 84 q^{17} - 42 q^{18} - 42 q^{19} - 42 q^{20} - 42 q^{22} - 42 q^{23} - 42 q^{24} - 84 q^{25} - 42 q^{26} - 42 q^{27} - 42 q^{28} - 42 q^{30} - 42 q^{31} - 42 q^{32} - 84 q^{33} - 42 q^{34} - 42 q^{35} - 42 q^{36} - 42 q^{38} - 42 q^{39} - 42 q^{40} - 84 q^{41} - 42 q^{42} - 42 q^{43} - 84 q^{44} - 42 q^{46} - 42 q^{47} - 42 q^{48} - 84 q^{49} - 42 q^{50} - 42 q^{51} - 42 q^{52} - 42 q^{54} - 42 q^{55} - 42 q^{56} - 84 q^{57} - 42 q^{58} - 42 q^{59} - 42 q^{60} - 42 q^{62} - 42 q^{63} - 42 q^{64} - 84 q^{65} - 42 q^{66} - 42 q^{67} - 42 q^{68} - 42 q^{69} - 42 q^{70} - 84 q^{71} - 42 q^{72} - 126 q^{73} - 42 q^{74} - 189 q^{75} - 42 q^{76} - 126 q^{77} - 42 q^{78} - 126 q^{79} - 42 q^{80} - 252 q^{81} - 42 q^{82} - 126 q^{83} - 42 q^{84} - 84 q^{85} - 42 q^{86} - 294 q^{87} - 42 q^{88} - 168 q^{89} - 42 q^{90} - 126 q^{91} - 42 q^{92} - 168 q^{93} - 42 q^{94} - 126 q^{95} - 42 q^{96} - 210 q^{97} - 42 q^{98} - 189 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)

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
344.2.a \(\chi_{344}(1, \cdot)\) 344.2.a.a 1 1
344.2.a.b 2
344.2.a.c 3
344.2.a.d 5
344.2.c \(\chi_{344}(173, \cdot)\) 344.2.c.a 42 1
344.2.e \(\chi_{344}(171, \cdot)\) 344.2.e.a 2 1
344.2.e.b 40
344.2.g \(\chi_{344}(343, \cdot)\) None 0 1
344.2.i \(\chi_{344}(49, \cdot)\) 344.2.i.a 2 2
344.2.i.b 2
344.2.i.c 8
344.2.i.d 10
344.2.k \(\chi_{344}(7, \cdot)\) None 0 2
344.2.m \(\chi_{344}(123, \cdot)\) 344.2.m.a 4 2
344.2.m.b 4
344.2.m.c 76
344.2.o \(\chi_{344}(165, \cdot)\) 344.2.o.a 84 2
344.2.q \(\chi_{344}(41, \cdot)\) 344.2.q.a 30 6
344.2.q.b 36
344.2.t \(\chi_{344}(39, \cdot)\) None 0 6
344.2.v \(\chi_{344}(27, \cdot)\) 344.2.v.a 12 6
344.2.v.b 240
344.2.x \(\chi_{344}(21, \cdot)\) 344.2.x.a 252 6
344.2.y \(\chi_{344}(9, \cdot)\) 344.2.y.a 60 12
344.2.y.b 72
344.2.z \(\chi_{344}(13, \cdot)\) 344.2.z.a 504 12
344.2.bb \(\chi_{344}(3, \cdot)\) 344.2.bb.a 24 12
344.2.bb.b 480
344.2.bd \(\chi_{344}(55, \cdot)\) None 0 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(344))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(344)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 1}\)