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Properties

Label 1352.4
Level 1352
Weight 4
Dimension 94284
Nonzero newspaces 20
Sturm bound 454272
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1352 = 2^{3} \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(454272\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1352))\).

Total New Old
Modular forms 171720 95102 76618
Cusp forms 168984 94284 74700
Eisenstein series 2736 818 1918

Trace form

\( 94284 q - 134 q^{2} - 136 q^{3} - 144 q^{4} - 2 q^{5} - 104 q^{6} - 124 q^{7} - 92 q^{8} - 277 q^{9} + O(q^{10}) \) \( 94284 q - 134 q^{2} - 136 q^{3} - 144 q^{4} - 2 q^{5} - 104 q^{6} - 124 q^{7} - 92 q^{8} - 277 q^{9} - 188 q^{10} - 176 q^{11} - 188 q^{12} - 236 q^{14} - 12 q^{15} - 116 q^{16} + 40 q^{17} - 130 q^{18} + 320 q^{19} - 20 q^{20} - 336 q^{21} - 216 q^{22} - 948 q^{23} - 244 q^{24} - 1109 q^{25} - 144 q^{26} - 1756 q^{27} - 36 q^{28} - 192 q^{29} - 244 q^{30} + 276 q^{31} - 484 q^{32} + 1568 q^{33} - 104 q^{34} + 1380 q^{35} - 768 q^{36} + 480 q^{37} - 328 q^{38} - 1404 q^{39} - 7804 q^{40} - 1664 q^{41} - 5972 q^{42} - 2096 q^{43} - 564 q^{44} + 832 q^{45} + 5212 q^{46} + 3300 q^{47} + 8028 q^{48} + 491 q^{49} + 10426 q^{50} + 6988 q^{51} + 5364 q^{52} + 3286 q^{53} + 10316 q^{54} + 5236 q^{55} + 6244 q^{56} + 456 q^{57} + 756 q^{58} - 1160 q^{59} - 5844 q^{60} - 2960 q^{61} - 7660 q^{62} - 1772 q^{63} - 14676 q^{64} + 1377 q^{65} - 15684 q^{66} - 2896 q^{67} + 36 q^{68} - 136 q^{69} - 2684 q^{70} - 2908 q^{71} - 172 q^{72} - 6170 q^{73} + 1156 q^{74} - 8816 q^{75} + 260 q^{76} - 8448 q^{77} - 144 q^{78} - 5436 q^{79} - 1476 q^{80} - 8325 q^{81} + 8 q^{82} - 5536 q^{83} + 8548 q^{84} - 6418 q^{85} + 17032 q^{86} - 22332 q^{87} + 16644 q^{88} - 2762 q^{89} + 24572 q^{90} - 2712 q^{91} + 5748 q^{92} + 11368 q^{93} - 3300 q^{94} + 17428 q^{95} - 20884 q^{96} + 5638 q^{97} - 15342 q^{98} + 32224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1352))\)

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
1352.4.a \(\chi_{1352}(1, \cdot)\) 1352.4.a.a 1 1
1352.4.a.b 1
1352.4.a.c 1
1352.4.a.d 1
1352.4.a.e 1
1352.4.a.f 2
1352.4.a.g 2
1352.4.a.h 3
1352.4.a.i 4
1352.4.a.j 4
1352.4.a.k 5
1352.4.a.l 5
1352.4.a.m 6
1352.4.a.n 6
1352.4.a.o 10
1352.4.a.p 10
1352.4.a.q 12
1352.4.a.r 12
1352.4.a.s 15
1352.4.a.t 15
1352.4.b \(\chi_{1352}(677, \cdot)\) n/a 454 1
1352.4.e \(\chi_{1352}(1013, \cdot)\) n/a 452 1
1352.4.f \(\chi_{1352}(337, \cdot)\) n/a 116 1
1352.4.i \(\chi_{1352}(529, \cdot)\) n/a 230 2
1352.4.k \(\chi_{1352}(239, \cdot)\) None 0 2
1352.4.m \(\chi_{1352}(99, \cdot)\) n/a 904 2
1352.4.o \(\chi_{1352}(361, \cdot)\) n/a 232 2
1352.4.r \(\chi_{1352}(653, \cdot)\) n/a 904 2
1352.4.s \(\chi_{1352}(485, \cdot)\) n/a 904 2
1352.4.u \(\chi_{1352}(19, \cdot)\) n/a 1808 4
1352.4.w \(\chi_{1352}(319, \cdot)\) None 0 4
1352.4.y \(\chi_{1352}(105, \cdot)\) n/a 1644 12
1352.4.bb \(\chi_{1352}(25, \cdot)\) n/a 1632 12
1352.4.bc \(\chi_{1352}(77, \cdot)\) n/a 6528 12
1352.4.bf \(\chi_{1352}(53, \cdot)\) n/a 6528 12
1352.4.bg \(\chi_{1352}(9, \cdot)\) n/a 3288 24
1352.4.bi \(\chi_{1352}(83, \cdot)\) n/a 13056 24
1352.4.bk \(\chi_{1352}(31, \cdot)\) None 0 24
1352.4.bm \(\chi_{1352}(69, \cdot)\) n/a 13056 24
1352.4.bn \(\chi_{1352}(29, \cdot)\) n/a 13056 24
1352.4.bq \(\chi_{1352}(17, \cdot)\) n/a 3264 24
1352.4.bs \(\chi_{1352}(7, \cdot)\) None 0 48
1352.4.bu \(\chi_{1352}(11, \cdot)\) n/a 26112 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1352))\) into lower level spaces

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