Properties

Label 441.4
Level 441
Weight 4
Dimension 15863
Nonzero newspaces 20
Sturm bound 56448
Trace bound 3

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Defining parameters

Level: \( N \) = \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(56448\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(441))\).

Total New Old
Modular forms 21648 16300 5348
Cusp forms 20688 15863 4825
Eisenstein series 960 437 523

Trace form

\( 15863q - 48q^{2} - 63q^{3} - 58q^{4} - 84q^{5} - 51q^{6} - 78q^{7} + 39q^{8} - 15q^{9} + O(q^{10}) \) \( 15863q - 48q^{2} - 63q^{3} - 58q^{4} - 84q^{5} - 51q^{6} - 78q^{7} + 39q^{8} - 15q^{9} - 69q^{10} - 111q^{11} - 312q^{12} - 398q^{13} - 606q^{14} - 321q^{15} - 94q^{16} + 573q^{17} + 828q^{18} + 1087q^{19} + 3153q^{20} + 288q^{21} + 1692q^{22} + 510q^{23} + 417q^{24} - 469q^{25} - 1731q^{26} - 1284q^{27} - 1794q^{28} - 2550q^{29} - 2952q^{30} - 3548q^{31} - 6402q^{32} - 1350q^{33} - 2232q^{34} - 66q^{35} + 987q^{36} + 463q^{37} + 4842q^{38} + 3219q^{39} + 5013q^{40} + 5565q^{41} + 2634q^{42} + 4039q^{43} + 11991q^{44} + 2049q^{45} + 9123q^{46} + 3468q^{47} + 4983q^{48} + 1908q^{49} + 2079q^{50} + 1749q^{51} - 6449q^{52} - 4893q^{53} - 4401q^{54} - 4341q^{55} - 5604q^{56} - 4401q^{57} + 1533q^{58} - 8283q^{59} - 17316q^{60} + 70q^{61} - 12543q^{62} - 5280q^{63} - 2527q^{64} - 9012q^{65} - 13566q^{66} - 3761q^{67} - 23460q^{68} - 10713q^{69} - 8823q^{70} - 7629q^{71} + 1083q^{72} - 7739q^{73} + 2205q^{74} + 12441q^{75} - 1550q^{76} + 8280q^{77} + 24894q^{78} + 10462q^{79} + 22422q^{80} + 12309q^{81} + 13374q^{82} + 11760q^{83} + 7596q^{84} + 16545q^{85} + 16179q^{86} + 2739q^{87} - 6759q^{88} + 627q^{89} - 1644q^{90} + 4323q^{91} - 2538q^{92} - 3633q^{93} + 7734q^{94} + 8151q^{95} - 5628q^{96} - 1562q^{97} + 19596q^{98} - 7863q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(441))\)

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
441.4.a \(\chi_{441}(1, \cdot)\) 441.4.a.a 1 1
441.4.a.b 1
441.4.a.c 1
441.4.a.d 1
441.4.a.e 1
441.4.a.f 1
441.4.a.g 1
441.4.a.h 1
441.4.a.i 1
441.4.a.j 1
441.4.a.k 1
441.4.a.l 1
441.4.a.m 1
441.4.a.n 2
441.4.a.o 2
441.4.a.p 2
441.4.a.q 2
441.4.a.r 2
441.4.a.s 3
441.4.a.t 3
441.4.a.u 4
441.4.a.v 4
441.4.a.w 4
441.4.a.x 8
441.4.c \(\chi_{441}(440, \cdot)\) 441.4.c.a 16 1
441.4.c.b 24
441.4.e \(\chi_{441}(226, \cdot)\) 441.4.e.a 2 2
441.4.e.b 2
441.4.e.c 2
441.4.e.d 2
441.4.e.e 2
441.4.e.f 2
441.4.e.g 2
441.4.e.h 2
441.4.e.i 2
441.4.e.j 2
441.4.e.k 2
441.4.e.l 2
441.4.e.m 2
441.4.e.n 2
441.4.e.o 2
441.4.e.p 4
441.4.e.q 4
441.4.e.r 4
441.4.e.s 4
441.4.e.t 4
441.4.e.u 4
441.4.e.v 4
441.4.e.w 6
441.4.e.x 8
441.4.e.y 8
441.4.e.z 16
441.4.f \(\chi_{441}(148, \cdot)\) n/a 236 2
441.4.g \(\chi_{441}(67, \cdot)\) n/a 232 2
441.4.h \(\chi_{441}(214, \cdot)\) n/a 232 2
441.4.i \(\chi_{441}(68, \cdot)\) n/a 232 2
441.4.o \(\chi_{441}(146, \cdot)\) n/a 232 2
441.4.p \(\chi_{441}(80, \cdot)\) 441.4.p.a 8 2
441.4.p.b 8
441.4.p.c 16
441.4.p.d 48
441.4.s \(\chi_{441}(362, \cdot)\) n/a 232 2
441.4.u \(\chi_{441}(64, \cdot)\) n/a 414 6
441.4.w \(\chi_{441}(62, \cdot)\) n/a 336 6
441.4.y \(\chi_{441}(25, \cdot)\) n/a 1992 12
441.4.z \(\chi_{441}(4, \cdot)\) n/a 1992 12
441.4.ba \(\chi_{441}(22, \cdot)\) n/a 1992 12
441.4.bb \(\chi_{441}(37, \cdot)\) n/a 828 12
441.4.bd \(\chi_{441}(47, \cdot)\) n/a 1992 12
441.4.bg \(\chi_{441}(17, \cdot)\) n/a 672 12
441.4.bh \(\chi_{441}(20, \cdot)\) n/a 1992 12
441.4.bn \(\chi_{441}(5, \cdot)\) n/a 1992 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)