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Properties

Label 441.7
Level 441
Weight 7
Dimension 31944
Nonzero newspaces 20
Sturm bound 98784
Trace bound 3

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Defining parameters

Level: \( N \) = \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(98784\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(441))\).

Total New Old
Modular forms 42816 32380 10436
Cusp forms 41856 31944 9912
Eisenstein series 960 436 524

Trace form

\( 31944 q - 48 q^{2} - 36 q^{3} - 114 q^{4} - 600 q^{5} + 273 q^{6} + 426 q^{7} + 1329 q^{8} - 2040 q^{9} + O(q^{10}) \) \( 31944 q - 48 q^{2} - 36 q^{3} - 114 q^{4} - 600 q^{5} + 273 q^{6} + 426 q^{7} + 1329 q^{8} - 2040 q^{9} - 7053 q^{10} - 7794 q^{11} - 1122 q^{12} + 19956 q^{13} - 7914 q^{14} - 16143 q^{15} + 16482 q^{16} + 56067 q^{17} + 59256 q^{18} - 2127 q^{19} - 63213 q^{20} - 22392 q^{21} - 69042 q^{22} - 118176 q^{23} - 17565 q^{24} - 93939 q^{25} + 175869 q^{26} + 76314 q^{27} + 254070 q^{28} + 105048 q^{29} - 18342 q^{30} + 43098 q^{31} - 561750 q^{32} - 186705 q^{33} - 612222 q^{34} - 104730 q^{35} + 272715 q^{36} + 739449 q^{37} + 1333992 q^{38} + 456711 q^{39} + 144363 q^{40} + 58176 q^{41} - 338322 q^{42} - 1261368 q^{43} - 1595559 q^{44} - 1261443 q^{45} - 533409 q^{46} - 54732 q^{47} - 1183287 q^{48} - 95994 q^{49} + 3130989 q^{50} + 3700938 q^{51} - 1567947 q^{52} + 1838715 q^{53} + 515619 q^{54} - 3524979 q^{55} - 1590390 q^{56} - 2243754 q^{57} + 5587995 q^{58} - 30450 q^{59} - 6728922 q^{60} + 2128302 q^{61} - 787983 q^{62} + 979032 q^{63} - 3079479 q^{64} + 4220970 q^{65} + 9150450 q^{66} - 1627452 q^{67} + 7287966 q^{68} + 394449 q^{69} - 3623049 q^{70} - 8397633 q^{71} - 13084413 q^{72} - 2010567 q^{73} - 7454625 q^{74} - 6929232 q^{75} + 15165438 q^{76} + 5958378 q^{77} + 11837664 q^{78} + 7284078 q^{79} + 31340580 q^{80} + 7957896 q^{81} - 3450948 q^{82} - 4034754 q^{83} - 1970100 q^{84} - 14161365 q^{85} - 11946261 q^{86} - 7173699 q^{87} - 22329477 q^{88} - 25571493 q^{89} - 24919458 q^{90} - 2860581 q^{91} - 20405646 q^{92} - 5238069 q^{93} + 21911028 q^{94} + 32361513 q^{95} + 27582108 q^{96} + 35144511 q^{97} + 19389912 q^{98} + 19115913 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(441))\)

We only show spaces with odd 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
441.7.b \(\chi_{441}(197, \cdot)\) 441.7.b.a 2 1
441.7.b.b 4
441.7.b.c 8
441.7.b.d 12
441.7.b.e 16
441.7.b.f 16
441.7.b.g 24
441.7.d \(\chi_{441}(244, \cdot)\) 441.7.d.a 2 1
441.7.d.b 4
441.7.d.c 8
441.7.d.d 8
441.7.d.e 12
441.7.d.f 16
441.7.d.g 24
441.7.d.h 24
441.7.j \(\chi_{441}(263, \cdot)\) n/a 472 2
441.7.k \(\chi_{441}(31, \cdot)\) n/a 472 2
441.7.l \(\chi_{441}(97, \cdot)\) n/a 472 2
441.7.m \(\chi_{441}(19, \cdot)\) n/a 196 2
441.7.n \(\chi_{441}(128, \cdot)\) n/a 472 2
441.7.q \(\chi_{441}(116, \cdot)\) n/a 160 2
441.7.r \(\chi_{441}(50, \cdot)\) n/a 482 2
441.7.t \(\chi_{441}(166, \cdot)\) n/a 472 2
441.7.v \(\chi_{441}(55, \cdot)\) n/a 834 6
441.7.x \(\chi_{441}(8, \cdot)\) n/a 672 6
441.7.bc \(\chi_{441}(40, \cdot)\) n/a 4008 12
441.7.be \(\chi_{441}(29, \cdot)\) n/a 4008 12
441.7.bf \(\chi_{441}(44, \cdot)\) n/a 1344 12
441.7.bi \(\chi_{441}(2, \cdot)\) n/a 4008 12
441.7.bj \(\chi_{441}(10, \cdot)\) n/a 1668 12
441.7.bk \(\chi_{441}(13, \cdot)\) n/a 4008 12
441.7.bl \(\chi_{441}(61, \cdot)\) n/a 4008 12
441.7.bm \(\chi_{441}(11, \cdot)\) n/a 4008 12

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

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