Properties

Label 25.9.c
Level $25$
Weight $9$
Character orbit 25.c
Rep. character $\chi_{25}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $22$
Newform subspaces $3$
Sturm bound $22$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(25, [\chi])\).

Total New Old
Modular forms 46 26 20
Cusp forms 34 22 12
Eisenstein series 12 4 8

Trace form

\( 22 q + 2 q^{2} + 72 q^{3} - 3516 q^{6} + 2352 q^{7} + 8220 q^{8} + O(q^{10}) \) \( 22 q + 2 q^{2} + 72 q^{3} - 3516 q^{6} + 2352 q^{7} + 8220 q^{8} - 46396 q^{11} + 45912 q^{12} + 119142 q^{13} - 699388 q^{16} + 265502 q^{17} + 454062 q^{18} - 873216 q^{21} + 35664 q^{22} - 28888 q^{23} + 4344524 q^{26} - 392040 q^{27} - 1305192 q^{28} - 1695176 q^{31} - 3033928 q^{32} - 4269096 q^{33} + 9851772 q^{36} + 454002 q^{37} - 1443720 q^{38} + 8145284 q^{41} - 4223856 q^{42} - 792648 q^{43} - 33395736 q^{46} + 15313352 q^{47} + 21677712 q^{48} - 19367916 q^{51} + 735732 q^{52} + 13509122 q^{53} - 23241360 q^{56} + 34625520 q^{57} + 23903520 q^{58} - 57062296 q^{61} - 53913416 q^{62} - 44837688 q^{63} + 223372788 q^{66} + 32827752 q^{67} - 8118692 q^{68} - 154125736 q^{71} - 82596420 q^{72} - 111859638 q^{73} + 358863380 q^{76} - 26260136 q^{77} - 31125576 q^{78} - 81460278 q^{81} - 38023056 q^{82} + 14768432 q^{83} + 23310944 q^{86} + 133207680 q^{87} + 44555040 q^{88} + 50148624 q^{91} - 69931048 q^{92} + 96798024 q^{93} - 1381059876 q^{96} + 186656202 q^{97} + 345959698 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.9.c.a 25.c 5.c $4$ $10.184$ \(\Q(i, \sqrt{141})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots\)
25.9.c.b 25.c 5.c $6$ $10.184$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2\) \(72\) \(0\) \(2352\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\)
25.9.c.c 25.c 5.c $12$ $10.184$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)