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Properties

Label 245.4.p
Level $245$
Weight $4$
Character orbit 245.p
Rep. character $\chi_{245}(29,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $492$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

Total New Old
Modular forms 516 516 0
Cusp forms 492 492 0
Eisenstein series 24 24 0

Trace form

\( 492 q + 310 q^{4} - 13 q^{5} + 2 q^{6} + 762 q^{9} + O(q^{10}) \) \( 492 q + 310 q^{4} - 13 q^{5} + 2 q^{6} + 762 q^{9} + 9 q^{10} + 102 q^{11} + 42 q^{14} - 353 q^{15} - 1314 q^{16} + 964 q^{19} - 387 q^{20} - 154 q^{21} - 86 q^{24} + 359 q^{25} + 74 q^{26} + 312 q^{29} + 336 q^{30} - 2752 q^{31} + 1346 q^{34} + 21 q^{35} - 3214 q^{36} + 442 q^{39} + 109 q^{40} + 726 q^{41} + 1810 q^{44} + 1007 q^{45} + 2450 q^{46} - 868 q^{49} + 4214 q^{50} - 454 q^{51} + 604 q^{54} - 2483 q^{55} - 938 q^{56} + 1908 q^{59} + 4575 q^{60} - 2154 q^{61} + 6890 q^{64} + 277 q^{65} + 504 q^{66} - 4822 q^{69} - 6937 q^{70} + 5282 q^{71} - 574 q^{74} - 6733 q^{75} - 8948 q^{76} + 2328 q^{79} + 11080 q^{80} + 2474 q^{81} - 798 q^{84} - 3923 q^{85} + 602 q^{86} - 8042 q^{89} - 3620 q^{90} + 5600 q^{91} - 7126 q^{94} - 3206 q^{95} + 1940 q^{96} - 2844 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.4.p.a 245.p 245.p $492$ $14.455$ None \(0\) \(0\) \(-13\) \(0\) $\mathrm{SU}(2)[C_{14}]$