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Properties

Label 245.4.f
Level $245$
Weight $4$
Character orbit 245.f
Rep. character $\chi_{245}(48,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $112$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 184 128 56
Cusp forms 152 112 40
Eisenstein series 32 16 16

Trace form

\( 112 q + 4 q^{2} - 124 q^{8} + O(q^{10}) \) \( 112 q + 4 q^{2} - 124 q^{8} + 48 q^{11} + 328 q^{15} - 1288 q^{16} - 72 q^{18} - 24 q^{22} + 500 q^{23} + 372 q^{25} - 2088 q^{30} - 68 q^{32} - 3472 q^{36} + 100 q^{37} - 432 q^{43} + 24 q^{46} + 68 q^{50} + 1208 q^{51} - 212 q^{53} + 5156 q^{57} + 6596 q^{58} + 4276 q^{60} - 1476 q^{65} - 2932 q^{67} - 4432 q^{71} - 10624 q^{72} - 5632 q^{78} - 1448 q^{81} + 2848 q^{85} + 15040 q^{86} + 1160 q^{88} + 8972 q^{92} + 4908 q^{93} - 3428 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.4.f.a 245.f 35.f $40$ $14.455$ None 35.4.k.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
245.4.f.b 245.f 35.f $72$ $14.455$ None 245.4.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)