↑

Properties

Label 30.6.c
Level $30$
Weight $6$
Character orbit 30.c
Rep. character $\chi_{30}(19,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 30.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(30, [\chi])\).

Total New Old
Modular forms 34 6 28
Cusp forms 26 6 20
Eisenstein series 8 0 8

Trace form

\( 6 q - 96 q^{4} - 104 q^{5} + 72 q^{6} - 486 q^{9} + O(q^{10}) \) \( 6 q - 96 q^{4} - 104 q^{5} + 72 q^{6} - 486 q^{9} - 72 q^{10} - 652 q^{11} - 880 q^{14} - 198 q^{15} + 1536 q^{16} + 2928 q^{19} + 1664 q^{20} + 2124 q^{21} - 1152 q^{24} - 4134 q^{25} + 2832 q^{26} + 10152 q^{29} + 4176 q^{30} + 12144 q^{31} - 24240 q^{34} - 37276 q^{35} + 7776 q^{36} - 16740 q^{39} + 1152 q^{40} + 11996 q^{41} + 10432 q^{44} + 8424 q^{45} + 2016 q^{46} - 37086 q^{49} - 21152 q^{50} - 36 q^{51} - 5832 q^{54} + 43032 q^{55} + 14080 q^{56} + 104060 q^{59} + 3168 q^{60} + 150828 q^{61} - 24576 q^{64} - 118812 q^{65} + 48528 q^{66} - 152136 q^{69} - 53088 q^{70} - 79752 q^{71} + 198992 q^{74} + 87192 q^{75} - 46848 q^{76} - 148896 q^{79} - 26624 q^{80} + 39366 q^{81} - 33984 q^{84} + 83604 q^{85} - 212576 q^{86} + 75484 q^{89} + 5832 q^{90} - 299208 q^{91} + 35328 q^{94} + 2400 q^{95} + 18432 q^{96} + 52812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
30.6.c.a 30.c 5.b $2$ $4.812$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-110\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{2}+9iq^{3}-2^{4}q^{4}+(-55+10i)q^{5}+\cdots\)
30.6.c.b 30.c 5.b $4$ $4.812$ \(\Q(i, \sqrt{1249})\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4\beta _{1}q^{2}+9\beta _{1}q^{3}-2^{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)