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Properties

Label 248.2
Level 248
Weight 2
Dimension 1020
Nonzero newspaces 12
Newform subspaces 29
Sturm bound 7680
Trace bound 7

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Defining parameters

Level: \( N \) = \( 248 = 2^{3} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 29 \)
Sturm bound: \(7680\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(248))\).

Total New Old
Modular forms 2100 1136 964
Cusp forms 1741 1020 721
Eisenstein series 359 116 243

Trace form

\( 1020 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{6} - 30 q^{7} - 30 q^{8} - 60 q^{9} + O(q^{10}) \) \( 1020 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{6} - 30 q^{7} - 30 q^{8} - 60 q^{9} - 30 q^{10} - 30 q^{11} - 30 q^{12} - 30 q^{14} - 30 q^{15} - 30 q^{16} - 60 q^{17} - 30 q^{18} - 30 q^{19} - 30 q^{20} - 30 q^{22} - 30 q^{23} - 30 q^{24} - 60 q^{25} - 30 q^{26} - 30 q^{27} - 30 q^{28} - 30 q^{30} - 30 q^{31} - 60 q^{32} - 60 q^{33} - 30 q^{34} - 30 q^{35} - 30 q^{36} - 30 q^{38} - 30 q^{39} - 30 q^{40} - 60 q^{41} - 30 q^{42} - 30 q^{43} - 30 q^{44} - 30 q^{46} - 30 q^{47} - 30 q^{48} - 90 q^{49} - 30 q^{50} - 120 q^{51} - 30 q^{52} - 30 q^{53} - 30 q^{54} - 90 q^{55} - 30 q^{56} - 150 q^{57} - 30 q^{58} - 60 q^{59} - 30 q^{60} - 90 q^{61} - 30 q^{62} - 180 q^{63} - 30 q^{64} - 150 q^{65} - 30 q^{66} - 60 q^{67} - 30 q^{68} - 90 q^{69} - 30 q^{70} - 90 q^{71} - 30 q^{72} - 90 q^{73} - 30 q^{74} - 120 q^{75} - 30 q^{76} - 30 q^{77} - 30 q^{78} - 30 q^{79} - 30 q^{80} - 60 q^{81} - 30 q^{82} - 30 q^{83} - 30 q^{84} - 30 q^{86} - 30 q^{87} - 30 q^{88} - 60 q^{89} + 60 q^{90} - 30 q^{91} - 30 q^{92} - 60 q^{94} - 30 q^{95} - 30 q^{96} - 60 q^{97} - 30 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)

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
248.2.a \(\chi_{248}(1, \cdot)\) 248.2.a.a 1 1
248.2.a.b 1
248.2.a.c 1
248.2.a.d 2
248.2.a.e 3
248.2.b \(\chi_{248}(123, \cdot)\) 248.2.b.a 6 1
248.2.b.b 24
248.2.c \(\chi_{248}(125, \cdot)\) 248.2.c.a 12 1
248.2.c.b 18
248.2.h \(\chi_{248}(247, \cdot)\) None 0 1
248.2.i \(\chi_{248}(25, \cdot)\) 248.2.i.a 2 2
248.2.i.b 2
248.2.i.c 2
248.2.i.d 2
248.2.i.e 2
248.2.i.f 6
248.2.j \(\chi_{248}(33, \cdot)\) 248.2.j.a 16 4
248.2.j.b 16
248.2.k \(\chi_{248}(119, \cdot)\) None 0 2
248.2.p \(\chi_{248}(5, \cdot)\) 248.2.p.a 4 2
248.2.p.b 56
248.2.q \(\chi_{248}(99, \cdot)\) 248.2.q.a 4 2
248.2.q.b 4
248.2.q.c 4
248.2.q.d 48
248.2.t \(\chi_{248}(15, \cdot)\) None 0 4
248.2.u \(\chi_{248}(101, \cdot)\) 248.2.u.a 120 4
248.2.v \(\chi_{248}(27, \cdot)\) 248.2.v.a 120 4
248.2.y \(\chi_{248}(9, \cdot)\) 248.2.y.a 32 8
248.2.y.b 32
248.2.bb \(\chi_{248}(3, \cdot)\) 248.2.bb.a 240 8
248.2.bc \(\chi_{248}(45, \cdot)\) 248.2.bc.a 240 8
248.2.bd \(\chi_{248}(55, \cdot)\) None 0 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)