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Properties

Label 315.6
Level 315
Weight 6
Dimension 11880
Nonzero newspaces 30
Sturm bound 41472
Trace bound 9

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Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(41472\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(315))\).

Total New Old
Modular forms 17664 12152 5512
Cusp forms 16896 11880 5016
Eisenstein series 768 272 496

Trace form

\( 11880 q + 22 q^{2} - 56 q^{3} - 214 q^{4} + 288 q^{5} + 644 q^{6} + 2 q^{7} - 3630 q^{8} - 1912 q^{9} + O(q^{10}) \) \( 11880 q + 22 q^{2} - 56 q^{3} - 214 q^{4} + 288 q^{5} + 644 q^{6} + 2 q^{7} - 3630 q^{8} - 1912 q^{9} + 3202 q^{10} + 5908 q^{11} + 9992 q^{12} - 3552 q^{13} - 726 q^{14} - 5204 q^{15} + 6158 q^{16} - 11780 q^{17} - 29528 q^{18} + 3292 q^{19} + 1742 q^{20} + 1560 q^{21} + 6060 q^{22} + 43872 q^{23} + 50580 q^{24} + 24600 q^{25} - 15404 q^{26} - 30620 q^{27} + 42754 q^{28} - 8776 q^{29} - 62242 q^{30} - 135764 q^{31} - 59530 q^{32} + 91448 q^{33} + 166868 q^{34} + 47968 q^{35} - 8828 q^{36} + 143044 q^{37} - 35588 q^{38} - 100688 q^{39} - 181966 q^{40} - 319660 q^{41} - 146580 q^{42} - 83984 q^{43} + 216080 q^{44} + 206528 q^{45} - 56740 q^{46} + 25396 q^{47} + 304700 q^{48} + 278844 q^{49} + 481546 q^{50} + 103592 q^{51} + 848448 q^{52} - 270440 q^{53} - 959200 q^{54} - 268980 q^{55} - 991518 q^{56} - 563768 q^{57} - 731964 q^{58} - 280940 q^{59} + 84362 q^{60} - 213524 q^{61} + 1446120 q^{62} + 929772 q^{63} + 479326 q^{64} + 546004 q^{65} + 511948 q^{66} - 331564 q^{67} - 844036 q^{68} - 585912 q^{69} + 103914 q^{70} + 92984 q^{71} - 305616 q^{72} + 758184 q^{73} - 429052 q^{74} - 641216 q^{75} - 603996 q^{76} + 140088 q^{77} - 142576 q^{78} - 218172 q^{79} - 311374 q^{80} - 554392 q^{81} - 1039632 q^{82} - 795096 q^{83} - 594252 q^{84} - 952304 q^{85} + 84040 q^{86} + 454420 q^{87} - 1335012 q^{88} - 668040 q^{89} + 882838 q^{90} + 229308 q^{91} + 2544888 q^{92} + 2039316 q^{93} + 3937916 q^{94} + 1375054 q^{95} + 871312 q^{96} + 2063904 q^{97} + 730466 q^{98} - 1758728 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(315))\)

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
315.6.a \(\chi_{315}(1, \cdot)\) 315.6.a.a 1 1
315.6.a.b 2
315.6.a.c 2
315.6.a.d 2
315.6.a.e 2
315.6.a.f 2
315.6.a.g 2
315.6.a.h 2
315.6.a.i 3
315.6.a.j 4
315.6.a.k 4
315.6.a.l 4
315.6.a.m 4
315.6.a.n 4
315.6.a.o 6
315.6.a.p 6
315.6.b \(\chi_{315}(251, \cdot)\) 315.6.b.a 28 1
315.6.b.b 28
315.6.d \(\chi_{315}(64, \cdot)\) 315.6.d.a 14 1
315.6.d.b 14
315.6.d.c 18
315.6.d.d 28
315.6.g \(\chi_{315}(314, \cdot)\) 315.6.g.a 80 1
315.6.i \(\chi_{315}(106, \cdot)\) n/a 240 2
315.6.j \(\chi_{315}(46, \cdot)\) n/a 132 2
315.6.k \(\chi_{315}(16, \cdot)\) n/a 320 2
315.6.l \(\chi_{315}(121, \cdot)\) n/a 320 2
315.6.m \(\chi_{315}(8, \cdot)\) n/a 120 2
315.6.p \(\chi_{315}(118, \cdot)\) n/a 196 2
315.6.r \(\chi_{315}(184, \cdot)\) n/a 472 2
315.6.t \(\chi_{315}(101, \cdot)\) n/a 320 2
315.6.u \(\chi_{315}(59, \cdot)\) n/a 472 2
315.6.z \(\chi_{315}(104, \cdot)\) n/a 472 2
315.6.bb \(\chi_{315}(89, \cdot)\) n/a 160 2
315.6.be \(\chi_{315}(236, \cdot)\) n/a 320 2
315.6.bf \(\chi_{315}(109, \cdot)\) n/a 196 2
315.6.bh \(\chi_{315}(169, \cdot)\) n/a 360 2
315.6.bj \(\chi_{315}(26, \cdot)\) n/a 104 2
315.6.bl \(\chi_{315}(41, \cdot)\) n/a 320 2
315.6.bo \(\chi_{315}(4, \cdot)\) n/a 472 2
315.6.bq \(\chi_{315}(164, \cdot)\) n/a 472 2
315.6.bs \(\chi_{315}(52, \cdot)\) n/a 944 4
315.6.bv \(\chi_{315}(23, \cdot)\) n/a 944 4
315.6.bx \(\chi_{315}(2, \cdot)\) n/a 944 4
315.6.bz \(\chi_{315}(73, \cdot)\) n/a 392 4
315.6.cb \(\chi_{315}(13, \cdot)\) n/a 944 4
315.6.cc \(\chi_{315}(92, \cdot)\) n/a 720 4
315.6.ce \(\chi_{315}(53, \cdot)\) n/a 320 4
315.6.cg \(\chi_{315}(157, \cdot)\) n/a 944 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(315))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(315)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)