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Properties

Label 676.6
Level 676
Weight 6
Dimension 40712
Nonzero newspaces 12
Sturm bound 170352
Trace bound 3

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Defining parameters

Level: \( N \) = \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(170352\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(676))\).

Total New Old
Modular forms 71550 41120 30430
Cusp forms 70410 40712 29698
Eisenstein series 1140 408 732

Trace form

\( 40712 q - 66 q^{2} - 12 q^{3} - 66 q^{4} - 78 q^{5} - 66 q^{6} + 508 q^{7} - 66 q^{8} - 1527 q^{9} + O(q^{10}) \) \( 40712 q - 66 q^{2} - 12 q^{3} - 66 q^{4} - 78 q^{5} - 66 q^{6} + 508 q^{7} - 66 q^{8} - 1527 q^{9} - 66 q^{10} + 1608 q^{11} - 78 q^{12} + 1428 q^{13} - 126 q^{14} - 3024 q^{15} - 66 q^{16} - 10596 q^{17} - 2910 q^{18} + 9820 q^{19} + 22734 q^{20} + 23448 q^{21} + 1674 q^{22} - 10560 q^{23} - 48546 q^{24} - 19115 q^{25} - 18042 q^{26} - 26208 q^{27} - 6606 q^{28} + 16644 q^{29} + 69534 q^{30} - 3020 q^{31} + 76674 q^{32} + 21240 q^{33} + 26094 q^{34} - 492 q^{35} - 100434 q^{36} - 1904 q^{37} - 78 q^{38} + 12084 q^{39} + 82482 q^{40} + 89388 q^{41} - 138414 q^{42} + 40824 q^{43} - 127926 q^{44} + 1692 q^{45} - 85146 q^{46} - 101748 q^{47} + 104478 q^{48} - 308063 q^{49} + 253458 q^{50} + 122664 q^{51} + 137574 q^{52} - 181302 q^{53} + 165762 q^{54} - 137652 q^{55} - 47478 q^{56} + 70968 q^{57} - 265122 q^{58} + 70872 q^{59} - 567846 q^{60} + 428960 q^{61} - 695610 q^{62} + 150300 q^{63} - 78 q^{64} + 62991 q^{65} + 1095882 q^{66} + 275116 q^{67} + 832818 q^{68} + 382992 q^{69} + 467850 q^{70} + 9024 q^{71} - 63870 q^{72} - 240674 q^{73} - 597978 q^{74} - 826452 q^{75} - 665946 q^{76} - 944388 q^{77} - 667086 q^{78} - 620920 q^{79} - 985254 q^{80} - 176991 q^{81} - 143946 q^{82} + 56400 q^{83} + 687306 q^{84} + 795534 q^{85} + 1867770 q^{86} + 1207776 q^{87} + 1314570 q^{88} + 958134 q^{89} - 78 q^{90} + 371698 q^{91} - 379758 q^{92} - 370656 q^{93} - 1496634 q^{94} - 873384 q^{95} - 1819470 q^{96} + 261502 q^{97} + 109182 q^{98} - 337896 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(676))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
676.6.a \(\chi_{676}(1, \cdot)\) 676.6.a.a 1 1
676.6.a.b 1
676.6.a.c 1
676.6.a.d 3
676.6.a.e 6
676.6.a.f 6
676.6.a.g 6
676.6.a.h 10
676.6.a.i 15
676.6.a.j 15
676.6.d \(\chi_{676}(337, \cdot)\) 676.6.d.a 2 1
676.6.d.b 2
676.6.d.c 2
676.6.d.d 6
676.6.d.e 10
676.6.d.f 12
676.6.d.g 30
676.6.e \(\chi_{676}(529, \cdot)\) n/a 128 2
676.6.f \(\chi_{676}(99, \cdot)\) n/a 750 2
676.6.h \(\chi_{676}(361, \cdot)\) n/a 130 2
676.6.l \(\chi_{676}(19, \cdot)\) n/a 1500 4
676.6.m \(\chi_{676}(53, \cdot)\) n/a 924 12
676.6.n \(\chi_{676}(25, \cdot)\) n/a 912 12
676.6.q \(\chi_{676}(9, \cdot)\) n/a 1824 24
676.6.s \(\chi_{676}(31, \cdot)\) n/a 10872 24
676.6.v \(\chi_{676}(17, \cdot)\) n/a 1800 24
676.6.w \(\chi_{676}(7, \cdot)\) n/a 21744 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

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