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Properties

Label 1352.2
Level 1352
Weight 2
Dimension 31155
Nonzero newspaces 20
Sturm bound 227136
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1352 = 2^{3} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(227136\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1352))\).

Total New Old
Modular forms 58152 31973 26179
Cusp forms 55417 31155 24262
Eisenstein series 2735 818 1917

Trace form

\( 31155 q - 132 q^{2} - 132 q^{3} - 132 q^{4} - 132 q^{6} - 132 q^{7} - 132 q^{8} - 264 q^{9} + O(q^{10}) \) \( 31155 q - 132 q^{2} - 132 q^{3} - 132 q^{4} - 132 q^{6} - 132 q^{7} - 132 q^{8} - 264 q^{9} - 132 q^{10} - 132 q^{11} - 132 q^{12} - 252 q^{14} - 132 q^{15} - 132 q^{16} - 258 q^{17} - 132 q^{18} - 108 q^{19} - 132 q^{20} + 48 q^{21} - 132 q^{22} - 108 q^{23} - 132 q^{24} - 234 q^{25} - 144 q^{26} - 180 q^{27} - 132 q^{28} + 30 q^{29} - 132 q^{30} - 108 q^{31} - 132 q^{32} - 216 q^{33} - 132 q^{34} - 108 q^{35} - 204 q^{36} + 6 q^{37} - 132 q^{38} - 156 q^{39} - 348 q^{40} - 282 q^{41} - 276 q^{42} - 228 q^{43} - 252 q^{44} - 90 q^{45} - 372 q^{46} - 204 q^{47} - 324 q^{48} - 288 q^{49} - 348 q^{50} - 300 q^{51} - 252 q^{52} - 72 q^{53} - 348 q^{54} - 276 q^{55} - 348 q^{56} - 288 q^{57} - 324 q^{58} - 204 q^{59} - 372 q^{60} - 90 q^{61} - 252 q^{62} - 180 q^{63} - 276 q^{64} - 261 q^{65} - 348 q^{66} - 108 q^{67} - 132 q^{68} + 72 q^{69} - 252 q^{70} - 36 q^{71} - 132 q^{72} - 168 q^{73} - 132 q^{74} - 84 q^{75} - 132 q^{76} + 96 q^{77} - 144 q^{78} - 204 q^{79} - 132 q^{80} - 168 q^{81} - 132 q^{82} - 12 q^{83} + 36 q^{84} + 78 q^{85} - 36 q^{86} - 180 q^{87} - 12 q^{88} - 264 q^{89} + 180 q^{90} - 216 q^{91} - 108 q^{92} - 72 q^{93} + 60 q^{94} - 324 q^{95} + 300 q^{96} - 336 q^{97} + 84 q^{98} - 516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)

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
1352.2.a \(\chi_{1352}(1, \cdot)\) 1352.2.a.a 1 1
1352.2.a.b 1
1352.2.a.c 1
1352.2.a.d 2
1352.2.a.e 2
1352.2.a.f 2
1352.2.a.g 2
1352.2.a.h 2
1352.2.a.i 3
1352.2.a.j 3
1352.2.a.k 4
1352.2.a.l 4
1352.2.a.m 6
1352.2.a.n 6
1352.2.b \(\chi_{1352}(677, \cdot)\) n/a 144 1
1352.2.e \(\chi_{1352}(1013, \cdot)\) n/a 144 1
1352.2.f \(\chi_{1352}(337, \cdot)\) 1352.2.f.a 2 1
1352.2.f.b 2
1352.2.f.c 4
1352.2.f.d 4
1352.2.f.e 6
1352.2.f.f 8
1352.2.f.g 12
1352.2.i \(\chi_{1352}(529, \cdot)\) 1352.2.i.a 2 2
1352.2.i.b 2
1352.2.i.c 2
1352.2.i.d 4
1352.2.i.e 4
1352.2.i.f 4
1352.2.i.g 4
1352.2.i.h 4
1352.2.i.i 6
1352.2.i.j 6
1352.2.i.k 8
1352.2.i.l 8
1352.2.i.m 12
1352.2.i.n 12
1352.2.k \(\chi_{1352}(239, \cdot)\) None 0 2
1352.2.m \(\chi_{1352}(99, \cdot)\) n/a 288 2
1352.2.o \(\chi_{1352}(361, \cdot)\) 1352.2.o.a 4 2
1352.2.o.b 4
1352.2.o.c 8
1352.2.o.d 8
1352.2.o.e 8
1352.2.o.f 8
1352.2.o.g 12
1352.2.o.h 24
1352.2.r \(\chi_{1352}(653, \cdot)\) n/a 288 2
1352.2.s \(\chi_{1352}(485, \cdot)\) n/a 288 2
1352.2.u \(\chi_{1352}(19, \cdot)\) n/a 576 4
1352.2.w \(\chi_{1352}(319, \cdot)\) None 0 4
1352.2.y \(\chi_{1352}(105, \cdot)\) n/a 540 12
1352.2.bb \(\chi_{1352}(25, \cdot)\) n/a 552 12
1352.2.bc \(\chi_{1352}(77, \cdot)\) n/a 2160 12
1352.2.bf \(\chi_{1352}(53, \cdot)\) n/a 2160 12
1352.2.bg \(\chi_{1352}(9, \cdot)\) n/a 1080 24
1352.2.bi \(\chi_{1352}(83, \cdot)\) n/a 4320 24
1352.2.bk \(\chi_{1352}(31, \cdot)\) None 0 24
1352.2.bm \(\chi_{1352}(69, \cdot)\) n/a 4320 24
1352.2.bn \(\chi_{1352}(29, \cdot)\) n/a 4320 24
1352.2.bq \(\chi_{1352}(17, \cdot)\) n/a 1104 24
1352.2.bs \(\chi_{1352}(7, \cdot)\) None 0 48
1352.2.bu \(\chi_{1352}(11, \cdot)\) n/a 8640 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 1}\)