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Properties

Label 103.16
Level 103
Weight 16
Dimension 6577
Nonzero newspaces 4
Sturm bound 14144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 103 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(14144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(103))\).

Total New Old
Modular forms 6681 6677 4
Cusp forms 6579 6577 2
Eisenstein series 102 100 2

Trace form

\( 6577 q - 483 q^{2} + 6645 q^{3} - 27827 q^{4} - 104271 q^{5} + 1446285 q^{6} - 5644963 q^{7} + 8156109 q^{8} + 6279555 q^{9} + O(q^{10}) \) \( 6577 q - 483 q^{2} + 6645 q^{3} - 27827 q^{4} - 104271 q^{5} + 1446285 q^{6} - 5644963 q^{7} + 8156109 q^{8} + 6279555 q^{9} - 22511571 q^{10} - 41173755 q^{11} + 92993997 q^{12} + 380146625 q^{13} - 1219301043 q^{14} + 348928509 q^{15} + 2671894477 q^{16} - 3293056023 q^{17} + 1356394845 q^{18} - 3126514411 q^{19} - 1447407411 q^{20} + 18899165325 q^{21} - 8893520115 q^{22} - 18902232195 q^{23} - 27306823731 q^{24} + 55604251999 q^{25} + 82111681965 q^{26} - 117104402211 q^{27} - 78396537907 q^{28} + 73805136609 q^{29} + 75368568909 q^{30} - 143176967155 q^{31} + 309868167117 q^{32} + 137849560941 q^{33} - 711300090003 q^{34} - 294156364371 q^{35} + 87211168077 q^{36} + 2067304163057 q^{37} - 675327101811 q^{38} - 1272731071299 q^{39} + 425017497549 q^{40} - 3283948036455 q^{41} + 4082219721165 q^{42} + 984806218565 q^{43} - 571820401203 q^{44} + 327230268609 q^{45} - 4082882143155 q^{46} + 6821369905197 q^{47} - 8945502879795 q^{48} - 6437392724037 q^{49} + 12010518442749 q^{50} + 11025151394205 q^{51} + 5279477036237 q^{52} - 13594303311855 q^{53} - 25294550866611 q^{54} - 2145561715491 q^{55} + 23020402728909 q^{56} + 10467570077229 q^{57} + 15941909518509 q^{58} - 19717713631131 q^{59} + 4845919841229 q^{60} - 9863685253855 q^{61} - 30926224894515 q^{62} + 17723911632285 q^{63} - 20621115785267 q^{64} + 19809443286309 q^{65} + 29775505174221 q^{66} + 57675653250677 q^{67} - 45733961339187 q^{68} + 63284673218061 q^{69} - 63537774693171 q^{70} - 250100229829155 q^{71} - 25608735636531 q^{72} + 164342911026905 q^{73} + 446537699231277 q^{74} - 186163035863451 q^{75} - 43421031431731 q^{76} - 116210967897075 q^{77} - 274909911389619 q^{78} + 50826157388909 q^{79} + 139232423854029 q^{80} + 301960055940987 q^{81} - 709332775863315 q^{82} + 563473461780885 q^{83} - 2770805600243763 q^{84} + 2465737420532781 q^{85} - 6768614160030195 q^{86} + 560886216353985 q^{87} + 25155342562185165 q^{88} + 1027352928197529 q^{89} - 16631743548905043 q^{90} - 12605711122547945 q^{91} - 5101865709204531 q^{92} + 7990256190257949 q^{93} + 15929208468327117 q^{94} + 8025817837270107 q^{95} - 3192517633572915 q^{96} - 15248859150612655 q^{97} - 37408956061877091 q^{98} - 15344451262069989 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(103))\)

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
103.16.a \(\chi_{103}(1, \cdot)\) 103.16.a.a 61 1
103.16.a.b 66
103.16.c \(\chi_{103}(46, \cdot)\) n/a 258 2
103.16.e \(\chi_{103}(8, \cdot)\) n/a 2064 16
103.16.g \(\chi_{103}(2, \cdot)\) n/a 4128 32

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(103))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(103)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 1}\)