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Properties

Label 325.6
Level 325
Weight 6
Dimension 18899
Nonzero newspaces 24
Sturm bound 50400
Trace bound 3

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Defining parameters

Level: \( N \) = \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(50400\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(325))\).

Total New Old
Modular forms 21336 19349 1987
Cusp forms 20664 18899 1765
Eisenstein series 672 450 222

Trace form

\( 18899 q - 50 q^{2} - 74 q^{3} - 266 q^{4} - 206 q^{5} + 934 q^{6} + 412 q^{7} + 38 q^{8} - 1542 q^{9} + O(q^{10}) \) \( 18899 q - 50 q^{2} - 74 q^{3} - 266 q^{4} - 206 q^{5} + 934 q^{6} + 412 q^{7} + 38 q^{8} - 1542 q^{9} - 856 q^{10} + 800 q^{11} - 2496 q^{12} - 1068 q^{13} + 4040 q^{14} + 2364 q^{15} + 5734 q^{16} - 4147 q^{17} - 14636 q^{18} - 10150 q^{19} - 20596 q^{20} - 10800 q^{21} + 18508 q^{22} + 27058 q^{23} + 67690 q^{24} + 37934 q^{25} - 6276 q^{26} - 2912 q^{27} - 80576 q^{28} - 97333 q^{29} - 107756 q^{30} + 26156 q^{31} + 28136 q^{32} + 28872 q^{33} + 89286 q^{34} + 80664 q^{35} + 23274 q^{36} + 25891 q^{37} + 93892 q^{38} - 96012 q^{39} - 179672 q^{40} - 125787 q^{41} - 341888 q^{42} - 40488 q^{43} + 25756 q^{44} + 35474 q^{45} + 114554 q^{46} + 127172 q^{47} + 618138 q^{48} + 332178 q^{49} + 642996 q^{50} + 414540 q^{51} + 30000 q^{52} - 86942 q^{53} - 933184 q^{54} - 454444 q^{55} - 1205384 q^{56} - 1095064 q^{57} - 781626 q^{58} - 279488 q^{59} + 86012 q^{60} + 449009 q^{61} + 491698 q^{62} + 890768 q^{63} + 1003108 q^{64} + 250715 q^{65} + 1138844 q^{66} + 457070 q^{67} + 771600 q^{68} + 589528 q^{69} + 38788 q^{70} + 364842 q^{71} - 1040892 q^{72} - 634254 q^{73} - 1384646 q^{74} - 213596 q^{75} - 1210506 q^{76} - 260652 q^{77} - 588332 q^{78} + 714172 q^{79} + 877588 q^{80} + 1541070 q^{81} + 1505326 q^{82} - 80236 q^{83} - 1088680 q^{84} - 1362426 q^{85} - 1923364 q^{86} - 2235790 q^{87} - 2880128 q^{88} - 759672 q^{89} - 1508916 q^{90} + 381094 q^{91} + 1253120 q^{92} + 1185352 q^{93} + 925722 q^{94} + 847884 q^{95} + 183056 q^{96} + 1639358 q^{97} + 2170818 q^{98} + 1811076 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.6.a \(\chi_{325}(1, \cdot)\) 325.6.a.a 1 1
325.6.a.b 2
325.6.a.c 3
325.6.a.d 3
325.6.a.e 4
325.6.a.f 6
325.6.a.g 6
325.6.a.h 9
325.6.a.i 9
325.6.a.j 11
325.6.a.k 11
325.6.a.l 15
325.6.a.m 15
325.6.b \(\chi_{325}(274, \cdot)\) 325.6.b.a 2 1
325.6.b.b 4
325.6.b.c 6
325.6.b.d 6
325.6.b.e 8
325.6.b.f 12
325.6.b.g 12
325.6.b.h 18
325.6.b.i 22
325.6.c \(\chi_{325}(51, \cdot)\) n/a 108 1
325.6.d \(\chi_{325}(324, \cdot)\) n/a 104 1
325.6.e \(\chi_{325}(126, \cdot)\) n/a 216 2
325.6.f \(\chi_{325}(18, \cdot)\) n/a 206 2
325.6.k \(\chi_{325}(57, \cdot)\) n/a 206 2
325.6.l \(\chi_{325}(66, \cdot)\) n/a 600 4
325.6.m \(\chi_{325}(49, \cdot)\) n/a 208 2
325.6.n \(\chi_{325}(101, \cdot)\) n/a 214 2
325.6.o \(\chi_{325}(74, \cdot)\) n/a 204 2
325.6.p \(\chi_{325}(64, \cdot)\) n/a 688 4
325.6.q \(\chi_{325}(116, \cdot)\) n/a 696 4
325.6.r \(\chi_{325}(14, \cdot)\) n/a 600 4
325.6.s \(\chi_{325}(32, \cdot)\) n/a 412 4
325.6.x \(\chi_{325}(7, \cdot)\) n/a 412 4
325.6.y \(\chi_{325}(16, \cdot)\) n/a 1376 8
325.6.z \(\chi_{325}(8, \cdot)\) n/a 1384 8
325.6.be \(\chi_{325}(47, \cdot)\) n/a 1384 8
325.6.bf \(\chi_{325}(9, \cdot)\) n/a 1392 8
325.6.bg \(\chi_{325}(36, \cdot)\) n/a 1392 8
325.6.bh \(\chi_{325}(4, \cdot)\) n/a 1376 8
325.6.bi \(\chi_{325}(28, \cdot)\) n/a 2768 16
325.6.bn \(\chi_{325}(2, \cdot)\) n/a 2768 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(325)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 1}\)