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Properties

Label 3152.2
Level 3152
Weight 2
Dimension 173750
Nonzero newspaces 21
Sturm bound 1241856
Trace bound 29

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Defining parameters

Level: \( N \) = \( 3152 = 2^{4} \cdot 197 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 21 \)
Sturm bound: \(1241856\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3152))\).

Total New Old
Modular forms 313208 175504 137704
Cusp forms 307721 173750 133971
Eisenstein series 5487 1754 3733

Trace form

\( 173750 q - 388 q^{2} - 290 q^{3} - 392 q^{4} - 486 q^{5} - 400 q^{6} - 294 q^{7} - 400 q^{8} - 98 q^{9} + O(q^{10}) \) \( 173750 q - 388 q^{2} - 290 q^{3} - 392 q^{4} - 486 q^{5} - 400 q^{6} - 294 q^{7} - 400 q^{8} - 98 q^{9} - 392 q^{10} - 298 q^{11} - 384 q^{12} - 486 q^{13} - 384 q^{14} - 302 q^{15} - 376 q^{16} - 874 q^{17} - 396 q^{18} - 306 q^{19} - 400 q^{20} - 498 q^{21} - 392 q^{22} - 294 q^{23} - 392 q^{24} - 98 q^{25} - 400 q^{26} - 278 q^{27} - 408 q^{28} - 502 q^{29} - 384 q^{30} - 262 q^{31} - 408 q^{32} - 874 q^{33} - 400 q^{34} - 286 q^{35} - 384 q^{36} - 502 q^{37} - 368 q^{38} - 294 q^{39} - 376 q^{40} - 98 q^{41} - 392 q^{42} - 314 q^{43} - 384 q^{44} - 494 q^{45} - 416 q^{46} - 326 q^{47} - 408 q^{48} - 894 q^{49} - 380 q^{50} - 302 q^{51} - 384 q^{52} - 470 q^{53} - 392 q^{54} - 294 q^{55} - 376 q^{56} - 98 q^{57} - 368 q^{58} - 282 q^{59} - 392 q^{60} - 454 q^{61} - 424 q^{62} - 302 q^{63} - 392 q^{64} - 890 q^{65} - 400 q^{66} - 274 q^{67} - 392 q^{68} - 466 q^{69} - 408 q^{70} - 294 q^{71} - 400 q^{72} - 98 q^{73} - 392 q^{74} - 306 q^{75} - 416 q^{76} - 498 q^{77} - 384 q^{78} - 294 q^{79} - 408 q^{80} - 902 q^{81} - 392 q^{82} - 290 q^{83} - 376 q^{84} - 498 q^{85} - 392 q^{86} - 294 q^{87} - 408 q^{88} - 98 q^{89} - 384 q^{90} - 302 q^{91} - 344 q^{92} - 522 q^{93} - 360 q^{94} - 270 q^{95} - 360 q^{96} - 874 q^{97} - 380 q^{98} - 290 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3152))\)

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
3152.2.a \(\chi_{3152}(1, \cdot)\) 3152.2.a.a 1 1
3152.2.a.b 1
3152.2.a.c 2
3152.2.a.d 2
3152.2.a.e 2
3152.2.a.f 2
3152.2.a.g 2
3152.2.a.h 4
3152.2.a.i 4
3152.2.a.j 5
3152.2.a.k 6
3152.2.a.l 9
3152.2.a.m 10
3152.2.a.n 10
3152.2.a.o 12
3152.2.a.p 12
3152.2.a.q 14
3152.2.b \(\chi_{3152}(1969, \cdot)\) 3152.2.b.a 4 1
3152.2.b.b 12
3152.2.b.c 16
3152.2.b.d 16
3152.2.b.e 50
3152.2.c \(\chi_{3152}(1577, \cdot)\) None 0 1
3152.2.h \(\chi_{3152}(393, \cdot)\) None 0 1
3152.2.i \(\chi_{3152}(211, \cdot)\) n/a 788 2
3152.2.m \(\chi_{3152}(1181, \cdot)\) n/a 788 2
3152.2.n \(\chi_{3152}(789, \cdot)\) n/a 784 2
3152.2.q \(\chi_{3152}(183, \cdot)\) None 0 2
3152.2.r \(\chi_{3152}(1759, \cdot)\) n/a 198 2
3152.2.t \(\chi_{3152}(1787, \cdot)\) n/a 788 2
3152.2.u \(\chi_{3152}(705, \cdot)\) n/a 588 6
3152.2.v \(\chi_{3152}(1385, \cdot)\) None 0 6
3152.2.ba \(\chi_{3152}(233, \cdot)\) None 0 6
3152.2.bb \(\chi_{3152}(33, \cdot)\) n/a 588 6
3152.2.bc \(\chi_{3152}(507, \cdot)\) n/a 4728 12
3152.2.be \(\chi_{3152}(87, \cdot)\) None 0 12
3152.2.bf \(\chi_{3152}(463, \cdot)\) n/a 1188 12
3152.2.bi \(\chi_{3152}(301, \cdot)\) n/a 4728 12
3152.2.bj \(\chi_{3152}(93, \cdot)\) n/a 4728 12
3152.2.bn \(\chi_{3152}(307, \cdot)\) n/a 4728 12
3152.2.bo \(\chi_{3152}(49, \cdot)\) n/a 4116 42
3152.2.bq \(\chi_{3152}(65, \cdot)\) n/a 4116 42
3152.2.bt \(\chi_{3152}(9, \cdot)\) None 0 42
3152.2.bv \(\chi_{3152}(105, \cdot)\) None 0 42
3152.2.bx \(\chi_{3152}(31, \cdot)\) n/a 8316 84
3152.2.bz \(\chi_{3152}(109, \cdot)\) n/a 33096 84
3152.2.ca \(\chi_{3152}(29, \cdot)\) n/a 33096 84
3152.2.cd \(\chi_{3152}(3, \cdot)\) n/a 33096 84
3152.2.cf \(\chi_{3152}(11, \cdot)\) n/a 33096 84
3152.2.cg \(\chi_{3152}(71, \cdot)\) None 0 84

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3152)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(197))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(394))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(788))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3152))\)\(^{\oplus 1}\)