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Properties

Label 27.7
Level 27
Weight 7
Dimension 120
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 378
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(378\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(27))\).

Total New Old
Modular forms 177 136 41
Cusp forms 147 120 27
Eisenstein series 30 16 14

Trace form

\( 120 q - 3 q^{2} - 6 q^{3} - 69 q^{4} + 429 q^{5} - 342 q^{6} - 1011 q^{7} - 9 q^{8} + 1242 q^{9} + O(q^{10}) \) \( 120 q - 3 q^{2} - 6 q^{3} - 69 q^{4} + 429 q^{5} - 342 q^{6} - 1011 q^{7} - 9 q^{8} + 1242 q^{9} + 3483 q^{10} - 975 q^{11} + 3549 q^{12} - 1227 q^{13} - 24357 q^{14} - 7974 q^{15} - 4893 q^{16} - 9 q^{17} + 40995 q^{18} + 13533 q^{19} + 43419 q^{20} - 2406 q^{21} - 29421 q^{22} - 39099 q^{23} + 35352 q^{24} - 78126 q^{25} + 64548 q^{27} + 167370 q^{28} + 34989 q^{29} - 186003 q^{30} - 51123 q^{31} - 358839 q^{32} - 78804 q^{33} - 213849 q^{34} + 268263 q^{35} + 412632 q^{36} + 255237 q^{37} + 400305 q^{38} + 126402 q^{39} - 149301 q^{40} + 2697 q^{41} - 466074 q^{42} - 81363 q^{43} - 1222785 q^{44} - 646578 q^{45} - 33075 q^{46} + 659985 q^{47} + 1608681 q^{48} - 70128 q^{49} + 1392204 q^{50} + 825291 q^{51} + 91671 q^{52} - 1089018 q^{54} - 267174 q^{55} - 3510471 q^{56} - 1657317 q^{57} + 612423 q^{58} + 764259 q^{59} - 168786 q^{60} + 479373 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 674661 q^{64} + 622725 q^{65} + 1054197 q^{66} - 1718211 q^{67} - 2285262 q^{68} - 3558150 q^{69} - 1368189 q^{70} - 427689 q^{71} - 419292 q^{72} - 1007067 q^{73} + 1863003 q^{74} + 3429390 q^{75} + 6633231 q^{76} + 7658493 q^{77} + 5939316 q^{78} + 3493653 q^{79} - 3002958 q^{81} - 5541354 q^{82} - 7934763 q^{83} - 10132716 q^{84} - 5554017 q^{85} - 8606307 q^{86} - 3444642 q^{87} - 1413045 q^{88} + 5907321 q^{89} + 5189148 q^{90} + 1229619 q^{91} + 1686261 q^{92} - 2952102 q^{93} + 10050543 q^{94} + 383835 q^{95} + 809838 q^{96} - 369723 q^{97} + 1179270 q^{98} + 1743822 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.7.b \(\chi_{27}(26, \cdot)\) 27.7.b.a 2 1
27.7.b.b 2
27.7.b.c 4
27.7.d \(\chi_{27}(8, \cdot)\) 27.7.d.a 10 2
27.7.f \(\chi_{27}(2, \cdot)\) 27.7.f.a 102 6

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 1}\)