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Properties

Label 153.10
Level 153
Weight 10
Dimension 6046
Nonzero newspaces 10
Sturm bound 17280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(17280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(153))\).

Total New Old
Modular forms 7904 6180 1724
Cusp forms 7648 6046 1602
Eisenstein series 256 134 122

Trace form

\( 6046 q - 90 q^{2} - 26 q^{3} + 3394 q^{4} - 6618 q^{5} - 4910 q^{6} + 16526 q^{7} - 15852 q^{8} + 31306 q^{9} + O(q^{10}) \) \( 6046 q - 90 q^{2} - 26 q^{3} + 3394 q^{4} - 6618 q^{5} - 4910 q^{6} + 16526 q^{7} - 15852 q^{8} + 31306 q^{9} - 72424 q^{10} - 183236 q^{11} + 482392 q^{12} + 127878 q^{13} + 346616 q^{14} - 1447718 q^{15} - 1344062 q^{16} + 351010 q^{17} + 2078936 q^{18} + 1930380 q^{19} - 2622112 q^{20} + 1006918 q^{21} - 6585670 q^{22} - 9141158 q^{23} + 5372086 q^{24} + 20011004 q^{25} - 19357152 q^{26} + 12353008 q^{27} + 4493840 q^{28} + 13347478 q^{29} - 61427120 q^{30} - 10430314 q^{31} - 19198846 q^{32} + 39862912 q^{33} - 53525373 q^{34} + 43920388 q^{35} + 97788154 q^{36} + 57234524 q^{37} + 148049834 q^{38} - 299630094 q^{39} - 274421592 q^{40} + 9587824 q^{41} + 312627196 q^{42} + 118802864 q^{43} + 454441204 q^{44} + 9171902 q^{45} - 544688520 q^{46} - 451676922 q^{47} - 397458406 q^{48} + 132250548 q^{49} + 449089662 q^{50} + 347451983 q^{51} + 854217980 q^{52} + 808735596 q^{53} + 402052622 q^{54} - 555361076 q^{55} - 3489229084 q^{56} - 1510781682 q^{57} - 1075367816 q^{58} + 216623764 q^{59} + 3031044312 q^{60} + 1738657322 q^{61} + 2340639544 q^{62} + 458799082 q^{63} - 1948682236 q^{64} - 1687221426 q^{65} - 2081048468 q^{66} - 1646696312 q^{67} - 3241315855 q^{68} + 1449512594 q^{69} + 2723865628 q^{70} + 2829294504 q^{71} + 3462874346 q^{72} - 920128276 q^{73} - 911260032 q^{74} - 2955380858 q^{75} - 1498169322 q^{76} - 1408769714 q^{77} - 486047948 q^{78} + 1117291530 q^{79} + 6225263144 q^{80} + 2110756450 q^{81} + 1256003252 q^{82} + 4932143722 q^{83} - 5999102964 q^{84} - 15246146826 q^{85} - 17410014818 q^{86} + 538745842 q^{87} + 13952370066 q^{88} + 19652822592 q^{89} + 16525303192 q^{90} + 9836116828 q^{91} - 4510273004 q^{92} - 6890344494 q^{93} - 19544423832 q^{94} - 22676062544 q^{95} - 21935579632 q^{96} - 8726869312 q^{97} - 2336347056 q^{98} + 5232003790 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(153))\)

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
153.10.a \(\chi_{153}(1, \cdot)\) 153.10.a.a 5 1
153.10.a.b 5
153.10.a.c 5
153.10.a.d 7
153.10.a.e 7
153.10.a.f 7
153.10.a.g 12
153.10.a.h 12
153.10.d \(\chi_{153}(118, \cdot)\) 153.10.d.a 2 1
153.10.d.b 12
153.10.d.c 24
153.10.d.d 28
153.10.e \(\chi_{153}(52, \cdot)\) n/a 288 2
153.10.f \(\chi_{153}(55, \cdot)\) n/a 132 2
153.10.h \(\chi_{153}(16, \cdot)\) n/a 320 2
153.10.l \(\chi_{153}(19, \cdot)\) n/a 268 4
153.10.n \(\chi_{153}(4, \cdot)\) n/a 640 4
153.10.o \(\chi_{153}(44, \cdot)\) n/a 432 8
153.10.r \(\chi_{153}(25, \cdot)\) n/a 1280 8
153.10.s \(\chi_{153}(5, \cdot)\) n/a 2560 16

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(153))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(153)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)