Properties

Label 30.4.c
Level $30$
Weight $4$
Character orbit 30.c
Rep. character $\chi_{30}(19,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 30.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(30, [\chi])\).

Total New Old
Modular forms 22 2 20
Cusp forms 14 2 12
Eisenstein series 8 0 8

Trace form

\( 2 q - 8 q^{4} + 4 q^{5} - 12 q^{6} - 18 q^{9} + O(q^{10}) \) \( 2 q - 8 q^{4} + 4 q^{5} - 12 q^{6} - 18 q^{9} - 44 q^{10} + 140 q^{11} + 8 q^{14} - 66 q^{15} + 32 q^{16} - 48 q^{19} - 16 q^{20} + 12 q^{21} + 48 q^{24} - 234 q^{25} + 216 q^{26} - 432 q^{29} - 24 q^{30} + 416 q^{31} + 88 q^{34} + 44 q^{35} + 72 q^{36} + 324 q^{39} + 176 q^{40} - 412 q^{41} - 560 q^{44} - 36 q^{45} - 400 q^{46} + 678 q^{49} - 176 q^{50} + 132 q^{51} + 108 q^{54} + 280 q^{55} - 32 q^{56} + 740 q^{59} + 264 q^{60} - 1100 q^{61} - 128 q^{64} + 1188 q^{65} - 840 q^{66} - 600 q^{69} + 16 q^{70} - 1080 q^{71} + 1016 q^{74} - 264 q^{75} + 192 q^{76} - 1584 q^{79} + 64 q^{80} + 162 q^{81} - 48 q^{84} + 484 q^{85} + 1168 q^{86} + 1876 q^{89} + 396 q^{90} - 216 q^{91} + 1280 q^{94} - 96 q^{95} - 192 q^{96} - 1260 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
30.4.c.a $2$ $1.770$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}+(2+11i)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)