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Properties

Label 2527.2
Level 2527
Weight 2
Dimension 245371
Nonzero newspaces 32
Sturm bound 1039680
Trace bound 10

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Defining parameters

Level: \( N \) = \( 2527 = 7 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1039680\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2527))\).

Total New Old
Modular forms 262944 250055 12889
Cusp forms 256897 245371 11526
Eisenstein series 6047 4684 1363

Trace form

\( 245371 q - 609 q^{2} - 608 q^{3} - 605 q^{4} - 606 q^{5} - 600 q^{6} - 764 q^{7} - 1515 q^{8} - 599 q^{9} + O(q^{10}) \) \( 245371 q - 609 q^{2} - 608 q^{3} - 605 q^{4} - 606 q^{5} - 600 q^{6} - 764 q^{7} - 1515 q^{8} - 599 q^{9} - 594 q^{10} - 600 q^{11} - 632 q^{12} - 646 q^{13} - 798 q^{14} - 1578 q^{15} - 725 q^{16} - 630 q^{17} - 717 q^{18} - 690 q^{19} - 1290 q^{20} - 803 q^{21} - 1602 q^{22} - 624 q^{23} - 696 q^{24} - 653 q^{25} - 642 q^{26} - 656 q^{27} - 836 q^{28} - 1572 q^{29} - 792 q^{30} - 652 q^{31} - 729 q^{32} - 780 q^{33} - 738 q^{34} - 831 q^{35} - 1871 q^{36} - 682 q^{37} - 774 q^{38} - 1348 q^{39} - 846 q^{40} - 642 q^{41} - 933 q^{42} - 1642 q^{43} - 816 q^{44} - 858 q^{45} - 864 q^{46} - 744 q^{47} - 992 q^{48} - 800 q^{49} - 1833 q^{50} - 756 q^{51} - 778 q^{52} - 702 q^{53} - 816 q^{54} - 684 q^{55} - 984 q^{56} - 1710 q^{57} - 1242 q^{58} - 732 q^{59} - 1056 q^{60} - 814 q^{61} - 912 q^{62} - 920 q^{63} - 1955 q^{64} - 924 q^{65} - 1044 q^{66} - 916 q^{67} - 990 q^{68} - 912 q^{69} - 1035 q^{70} - 1710 q^{71} - 1209 q^{72} - 874 q^{73} - 858 q^{74} - 860 q^{75} - 828 q^{76} - 1671 q^{77} - 1938 q^{78} - 940 q^{79} - 1074 q^{80} - 959 q^{81} - 1170 q^{82} - 780 q^{83} - 1169 q^{84} - 1854 q^{85} - 876 q^{86} - 1068 q^{87} - 1080 q^{88} - 846 q^{89} - 1206 q^{90} - 919 q^{91} - 1830 q^{92} - 892 q^{93} - 936 q^{94} - 774 q^{95} - 1800 q^{96} - 766 q^{97} - 1104 q^{98} - 1914 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2527))\)

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
2527.2.a \(\chi_{2527}(1, \cdot)\) 2527.2.a.a 2 1
2527.2.a.b 2
2527.2.a.c 2
2527.2.a.d 2
2527.2.a.e 2
2527.2.a.f 3
2527.2.a.g 3
2527.2.a.h 3
2527.2.a.i 4
2527.2.a.j 5
2527.2.a.k 5
2527.2.a.l 6
2527.2.a.m 6
2527.2.a.n 6
2527.2.a.o 10
2527.2.a.p 10
2527.2.a.q 15
2527.2.a.r 15
2527.2.a.s 15
2527.2.a.t 15
2527.2.a.u 16
2527.2.a.v 24
2527.2.c \(\chi_{2527}(2526, \cdot)\) n/a 212 1
2527.2.e \(\chi_{2527}(2234, \cdot)\) n/a 340 2
2527.2.f \(\chi_{2527}(723, \cdot)\) n/a 420 2
2527.2.g \(\chi_{2527}(429, \cdot)\) n/a 420 2
2527.2.h \(\chi_{2527}(653, \cdot)\) n/a 420 2
2527.2.i \(\chi_{2527}(654, \cdot)\) n/a 420 2
2527.2.o \(\chi_{2527}(360, \cdot)\) n/a 420 2
2527.2.p \(\chi_{2527}(69, \cdot)\) n/a 424 2
2527.2.s \(\chi_{2527}(430, \cdot)\) n/a 420 2
2527.2.u \(\chi_{2527}(606, \cdot)\) n/a 1266 6
2527.2.v \(\chi_{2527}(99, \cdot)\) n/a 1020 6
2527.2.w \(\chi_{2527}(389, \cdot)\) n/a 1266 6
2527.2.ba \(\chi_{2527}(307, \cdot)\) n/a 1260 6
2527.2.bb \(\chi_{2527}(488, \cdot)\) n/a 1266 6
2527.2.bf \(\chi_{2527}(262, \cdot)\) n/a 1266 6
2527.2.bg \(\chi_{2527}(134, \cdot)\) n/a 3420 18
2527.2.bi \(\chi_{2527}(132, \cdot)\) n/a 4500 18
2527.2.bk \(\chi_{2527}(11, \cdot)\) n/a 9072 36
2527.2.bl \(\chi_{2527}(30, \cdot)\) n/a 9072 36
2527.2.bm \(\chi_{2527}(39, \cdot)\) n/a 9072 36
2527.2.bn \(\chi_{2527}(64, \cdot)\) n/a 6840 36
2527.2.bp \(\chi_{2527}(31, \cdot)\) n/a 9072 36
2527.2.bs \(\chi_{2527}(27, \cdot)\) n/a 9000 36
2527.2.bt \(\chi_{2527}(75, \cdot)\) n/a 9072 36
2527.2.bz \(\chi_{2527}(12, \cdot)\) n/a 9072 36
2527.2.ca \(\chi_{2527}(4, \cdot)\) n/a 27108 108
2527.2.cb \(\chi_{2527}(36, \cdot)\) n/a 20520 108
2527.2.cc \(\chi_{2527}(9, \cdot)\) n/a 27108 108
2527.2.cd \(\chi_{2527}(10, \cdot)\) n/a 27108 108
2527.2.ch \(\chi_{2527}(3, \cdot)\) n/a 27108 108
2527.2.ci \(\chi_{2527}(13, \cdot)\) n/a 27216 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2527))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2527)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)