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Properties

Label 456.3
Level 456
Weight 3
Dimension 4764
Nonzero newspaces 18
Sturm bound 34560
Trace bound 6

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Defining parameters

Level: \( N \) = \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(34560\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(456))\).

Total New Old
Modular forms 11952 4900 7052
Cusp forms 11088 4764 6324
Eisenstein series 864 136 728

Trace form

\( 4764 q - 4 q^{2} - 22 q^{3} - 12 q^{4} + 10 q^{6} - 4 q^{7} + 8 q^{8} - 28 q^{9} + O(q^{10}) \) \( 4764 q - 4 q^{2} - 22 q^{3} - 12 q^{4} + 10 q^{6} - 4 q^{7} + 8 q^{8} - 28 q^{9} - 12 q^{10} + 64 q^{11} - 50 q^{12} - 40 q^{13} - 72 q^{14} - 42 q^{15} - 100 q^{16} + 16 q^{17} - 142 q^{18} - 72 q^{19} - 144 q^{20} + 24 q^{21} - 132 q^{22} + 86 q^{24} + 72 q^{25} + 192 q^{26} - 16 q^{27} + 316 q^{28} - 288 q^{29} + 326 q^{30} - 284 q^{31} + 176 q^{32} - 292 q^{33} + 100 q^{34} - 336 q^{35} - 234 q^{36} + 24 q^{37} - 40 q^{38} - 192 q^{39} - 532 q^{40} + 64 q^{41} - 458 q^{42} + 4 q^{43} - 128 q^{44} + 304 q^{45} - 340 q^{46} + 360 q^{47} + 126 q^{48} + 560 q^{49} + 236 q^{50} + 556 q^{51} + 284 q^{52} + 386 q^{54} + 556 q^{55} + 336 q^{56} - 48 q^{57} - 80 q^{58} + 256 q^{59} + 426 q^{60} + 848 q^{61} + 1932 q^{62} + 550 q^{63} + 2652 q^{64} + 888 q^{65} + 846 q^{66} + 2196 q^{67} + 1540 q^{68} + 128 q^{69} + 2044 q^{70} + 432 q^{71} + 554 q^{72} - 628 q^{73} + 528 q^{74} - 356 q^{75} - 324 q^{76} - 216 q^{77} - 238 q^{78} - 1844 q^{79} - 1248 q^{80} - 252 q^{81} - 3120 q^{82} - 1184 q^{83} - 2138 q^{84} - 512 q^{85} - 2948 q^{86} - 2298 q^{87} - 3684 q^{88} - 1112 q^{89} - 646 q^{90} - 2676 q^{91} - 3252 q^{92} - 236 q^{93} - 1068 q^{94} + 44 q^{96} + 8 q^{97} - 340 q^{98} + 928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.3.b \(\chi_{456}(455, \cdot)\) None 0 1
456.3.c \(\chi_{456}(115, \cdot)\) 456.3.c.a 72 1
456.3.h \(\chi_{456}(305, \cdot)\) 456.3.h.a 36 1
456.3.i \(\chi_{456}(37, \cdot)\) 456.3.i.a 80 1
456.3.l \(\chi_{456}(227, \cdot)\) n/a 156 1
456.3.m \(\chi_{456}(343, \cdot)\) None 0 1
456.3.n \(\chi_{456}(77, \cdot)\) n/a 144 1
456.3.o \(\chi_{456}(265, \cdot)\) 456.3.o.a 20 1
456.3.r \(\chi_{456}(7, \cdot)\) None 0 2
456.3.s \(\chi_{456}(107, \cdot)\) n/a 312 2
456.3.w \(\chi_{456}(145, \cdot)\) 456.3.w.a 20 2
456.3.w.b 20
456.3.x \(\chi_{456}(125, \cdot)\) n/a 312 2
456.3.ba \(\chi_{456}(163, \cdot)\) n/a 160 2
456.3.bb \(\chi_{456}(335, \cdot)\) None 0 2
456.3.bc \(\chi_{456}(373, \cdot)\) n/a 160 2
456.3.bd \(\chi_{456}(353, \cdot)\) 456.3.bd.a 80 2
456.3.bh \(\chi_{456}(5, \cdot)\) n/a 936 6
456.3.bi \(\chi_{456}(97, \cdot)\) n/a 120 6
456.3.bl \(\chi_{456}(17, \cdot)\) n/a 240 6
456.3.bn \(\chi_{456}(13, \cdot)\) n/a 480 6
456.3.bo \(\chi_{456}(71, \cdot)\) None 0 6
456.3.bq \(\chi_{456}(43, \cdot)\) n/a 480 6
456.3.bt \(\chi_{456}(59, \cdot)\) n/a 936 6
456.3.bv \(\chi_{456}(55, \cdot)\) None 0 6

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)