↑

Properties

Label 348.3.f
Level $348$
Weight $3$
Character orbit 348.f
Rep. character $\chi_{348}(175,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 348.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(348, [\chi])\).

Total New Old
Modular forms 124 56 68
Cusp forms 116 56 60
Eisenstein series 8 0 8

Trace form

\( 56 q - 4 q^{4} - 12 q^{6} - 12 q^{8} - 168 q^{9} + O(q^{10}) \) \( 56 q - 4 q^{4} - 12 q^{6} - 12 q^{8} - 168 q^{9} - 8 q^{10} + 24 q^{12} + 16 q^{13} + 76 q^{14} + 36 q^{16} - 16 q^{20} - 48 q^{21} - 110 q^{22} - 18 q^{24} + 280 q^{25} - 12 q^{26} - 138 q^{28} + 72 q^{30} + 120 q^{32} + 2 q^{34} + 12 q^{36} + 80 q^{37} - 32 q^{38} - 132 q^{40} - 32 q^{41} - 6 q^{42} + 316 q^{44} + 124 q^{46} - 344 q^{49} - 64 q^{50} - 78 q^{52} + 36 q^{54} - 208 q^{56} + 144 q^{57} - 120 q^{60} - 48 q^{61} + 64 q^{62} + 218 q^{64} - 160 q^{65} - 120 q^{66} - 164 q^{68} - 192 q^{69} - 580 q^{70} + 36 q^{72} - 240 q^{73} + 312 q^{74} + 120 q^{76} + 96 q^{77} - 90 q^{78} + 84 q^{80} + 504 q^{81} + 492 q^{82} + 72 q^{84} + 64 q^{85} + 372 q^{86} - 224 q^{88} + 224 q^{89} + 24 q^{90} + 28 q^{92} + 48 q^{93} - 186 q^{94} + 372 q^{96} + 336 q^{97} - 476 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(348, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
348.3.f.a 348.f 4.b $56$ $9.482$ None 348.3.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(348, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(348, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)