Properties

Label 306.4
Level 306
Weight 4
Dimension 2038
Nonzero newspaces 10
Sturm bound 20736
Trace bound 1

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Defining parameters

Level: \( N \) = \( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(20736\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(306))\).

Total New Old
Modular forms 8032 2038 5994
Cusp forms 7520 2038 5482
Eisenstein series 512 0 512

Trace form

\( 2038 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 8 q^{7} + 16 q^{8} + 210 q^{9} + O(q^{10}) \) \( 2038 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 8 q^{7} + 16 q^{8} + 210 q^{9} + 128 q^{10} + 170 q^{11} - 48 q^{12} - 92 q^{13} - 296 q^{14} - 180 q^{15} - 304 q^{17} - 312 q^{18} - 620 q^{19} - 112 q^{20} + 72 q^{21} + 308 q^{22} + 1280 q^{23} + 48 q^{24} + 2292 q^{25} + 928 q^{26} + 320 q^{28} + 496 q^{29} + 576 q^{30} - 676 q^{31} - 128 q^{32} - 1530 q^{33} - 342 q^{34} - 3848 q^{35} - 1032 q^{36} - 1564 q^{37} - 3268 q^{38} - 4084 q^{39} + 96 q^{40} - 4802 q^{41} - 480 q^{42} + 638 q^{43} + 1488 q^{44} + 3964 q^{45} + 2544 q^{46} + 10248 q^{47} + 288 q^{48} + 10560 q^{49} + 7528 q^{50} + 6553 q^{51} + 4496 q^{52} + 8360 q^{53} + 2348 q^{54} + 9848 q^{55} - 544 q^{56} - 694 q^{57} - 960 q^{58} - 4810 q^{59} - 688 q^{60} - 6800 q^{61} - 8128 q^{62} - 6588 q^{63} - 896 q^{64} - 15976 q^{65} - 3616 q^{66} - 6014 q^{67} + 92 q^{68} - 2988 q^{69} + 3216 q^{70} + 4464 q^{71} + 48 q^{72} + 3772 q^{73} - 1792 q^{74} - 6462 q^{75} + 680 q^{76} - 3224 q^{77} - 264 q^{78} + 1588 q^{79} + 320 q^{80} - 630 q^{81} + 696 q^{82} - 7660 q^{83} - 1488 q^{84} - 22876 q^{85} - 2244 q^{86} - 4056 q^{87} - 1968 q^{88} - 3204 q^{89} + 864 q^{90} - 9560 q^{91} + 3008 q^{92} + 8980 q^{93} - 1224 q^{94} + 20096 q^{95} - 768 q^{96} + 8018 q^{97} - 1332 q^{98} + 11376 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)

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
306.4.a \(\chi_{306}(1, \cdot)\) 306.4.a.a 1 1
306.4.a.b 1
306.4.a.c 1
306.4.a.d 1
306.4.a.e 1
306.4.a.f 1
306.4.a.g 1
306.4.a.h 1
306.4.a.i 2
306.4.a.j 2
306.4.a.k 2
306.4.a.l 3
306.4.a.m 3
306.4.b \(\chi_{306}(271, \cdot)\) 306.4.b.a 2 1
306.4.b.b 2
306.4.b.c 4
306.4.b.d 4
306.4.b.e 4
306.4.b.f 6
306.4.e \(\chi_{306}(103, \cdot)\) 306.4.e.a 4 2
306.4.e.b 18
306.4.e.c 22
306.4.e.d 26
306.4.e.e 26
306.4.g \(\chi_{306}(55, \cdot)\) 306.4.g.a 2 2
306.4.g.b 4
306.4.g.c 4
306.4.g.d 6
306.4.g.e 8
306.4.g.f 8
306.4.g.g 12
306.4.j \(\chi_{306}(67, \cdot)\) n/a 108 2
306.4.l \(\chi_{306}(19, \cdot)\) 306.4.l.a 8 4
306.4.l.b 12
306.4.l.c 16
306.4.l.d 16
306.4.l.e 20
306.4.l.f 20
306.4.n \(\chi_{306}(13, \cdot)\) n/a 216 4
306.4.o \(\chi_{306}(71, \cdot)\) n/a 144 8
306.4.r \(\chi_{306}(25, \cdot)\) n/a 432 8
306.4.s \(\chi_{306}(5, \cdot)\) n/a 864 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(306))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(306)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)