Properties

Label 225.6
Level 225
Weight 6
Dimension 6474
Nonzero newspaces 12
Sturm bound 21600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(21600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(225))\).

Total New Old
Modular forms 9224 6659 2565
Cusp forms 8776 6474 2302
Eisenstein series 448 185 263

Trace form

\( 6474q - 17q^{2} - 36q^{3} + 37q^{4} + 39q^{5} + 131q^{6} - 418q^{7} - 1212q^{8} - 686q^{9} + O(q^{10}) \) \( 6474q - 17q^{2} - 36q^{3} + 37q^{4} + 39q^{5} + 131q^{6} - 418q^{7} - 1212q^{8} - 686q^{9} + 2300q^{10} + 3298q^{11} + 2188q^{12} - 4330q^{13} - 13782q^{14} - 2204q^{15} - 6935q^{16} + 458q^{17} + 708q^{18} + 21926q^{19} + 16890q^{20} + 4470q^{21} + 6469q^{22} + 12650q^{23} + 25877q^{24} - 8823q^{25} - 40080q^{26} - 30384q^{27} - 63070q^{28} - 24674q^{29} - 32472q^{30} - 31438q^{31} + 1897q^{32} + 62644q^{33} + 52455q^{34} + 11408q^{35} - 58469q^{36} + 136395q^{37} - 15809q^{38} - 48396q^{39} + 36188q^{40} - 60032q^{41} + 109250q^{42} + 10906q^{43} + 229422q^{44} + 63108q^{45} - 340750q^{46} - 151858q^{47} + 8795q^{48} + 34192q^{49} - 56674q^{50} + 28924q^{51} + 420498q^{52} + 34723q^{53} - 254171q^{54} + 105218q^{55} - 283860q^{56} - 212370q^{57} - 450052q^{58} - 26608q^{59} + 288020q^{60} - 306110q^{61} - 496504q^{62} - 237336q^{63} - 838422q^{64} - 521387q^{65} + 127522q^{66} + 229826q^{67} + 658313q^{68} + 366838q^{69} + 786630q^{70} + 282602q^{71} + 1508883q^{72} + 129416q^{73} + 617324q^{74} + 471488q^{75} - 502695q^{76} - 177192q^{77} - 1148058q^{78} + 470838q^{79} - 842870q^{80} - 432038q^{81} - 1191188q^{82} - 1066232q^{83} - 714982q^{84} - 659899q^{85} + 424099q^{86} + 47032q^{87} - 1247619q^{88} + 913695q^{89} + 1828744q^{90} + 494202q^{91} + 4844416q^{92} + 2009878q^{93} + 477234q^{94} + 33370q^{95} - 102392q^{96} - 26636q^{97} - 2909162q^{98} - 2214624q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.6.a \(\chi_{225}(1, \cdot)\) 225.6.a.a 1 1
225.6.a.b 1
225.6.a.c 1
225.6.a.d 1
225.6.a.e 1
225.6.a.f 1
225.6.a.g 1
225.6.a.h 1
225.6.a.i 2
225.6.a.j 2
225.6.a.k 2
225.6.a.l 2
225.6.a.m 2
225.6.a.n 2
225.6.a.o 2
225.6.a.p 2
225.6.a.q 2
225.6.a.r 2
225.6.a.s 2
225.6.a.t 2
225.6.a.u 2
225.6.a.v 4
225.6.b \(\chi_{225}(199, \cdot)\) 225.6.b.a 2 1
225.6.b.b 2
225.6.b.c 2
225.6.b.d 2
225.6.b.e 2
225.6.b.f 2
225.6.b.g 4
225.6.b.h 4
225.6.b.i 4
225.6.b.j 4
225.6.b.k 4
225.6.b.l 4
225.6.e \(\chi_{225}(76, \cdot)\) n/a 184 2
225.6.f \(\chi_{225}(107, \cdot)\) 225.6.f.a 16 2
225.6.f.b 20
225.6.f.c 24
225.6.h \(\chi_{225}(46, \cdot)\) n/a 244 4
225.6.k \(\chi_{225}(49, \cdot)\) n/a 176 2
225.6.m \(\chi_{225}(19, \cdot)\) n/a 248 4
225.6.p \(\chi_{225}(32, \cdot)\) n/a 352 4
225.6.q \(\chi_{225}(16, \cdot)\) n/a 1184 8
225.6.s \(\chi_{225}(8, \cdot)\) n/a 400 8
225.6.u \(\chi_{225}(4, \cdot)\) n/a 1184 8
225.6.w \(\chi_{225}(2, \cdot)\) n/a 2368 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)