Properties

Label 25.34.b
Level $25$
Weight $34$
Character orbit 25.b
Rep. character $\chi_{25}(24,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $4$
Sturm bound $85$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 25.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(85\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(25, [\chi])\).

Total New Old
Modular forms 86 50 36
Cusp forms 80 48 32
Eisenstein series 6 2 4

Trace form

\( 48q - 189304795346q^{4} - 16344155009654q^{6} - 88843709186818414q^{9} + O(q^{10}) \) \( 48q - 189304795346q^{4} - 16344155009654q^{6} - 88843709186818414q^{9} - 395313248894571414q^{11} + 2422594115036596908q^{14} + 917466578268344886338q^{16} + 2070337530736198032830q^{19} - 24614790102063805942764q^{21} + 324779962521289241515890q^{24} - 563317182234034861520064q^{26} - 758916992764935433073580q^{29} + 2742578389969088111052716q^{31} + 69541638341963944556902798q^{34} + 316844286815529903747059828q^{36} + 1300053168681902195022686512q^{39} - 101050066658206457343345894q^{41} + 1365527165809683624372816078q^{44} - 6612157666573223087599205124q^{46} + 6084104657300297353883839664q^{49} - 6100975722682679767563687134q^{51} + 495711093787149831312700336130q^{54} + 132538109391288335079744680220q^{56} + 589264687828773075421346021640q^{59} + 220113703303751276269744691536q^{61} - 6365985146533162829697190230786q^{64} + 4314465860188742909708493448922q^{66} - 13036126514695856174835357542508q^{69} - 10493069708189310903017158919424q^{71} - 53594289067042452475372173420972q^{74} + 74706613528983596931454804425090q^{76} + 24858177510370750965976081061620q^{79} - 81438414611307874837774948874312q^{81} + 624046648976724143125242259514028q^{84} + 159751560945039428228587710082056q^{86} + 577312522671761460627909099259410q^{89} - 788178144282192462520177558680824q^{91} - 1809471639635906758613568641856632q^{94} + 342617643704611025444749137375806q^{96} - 490131131145430790146269196501148q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.34.b.a \(4\) \(172.457\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(78^{2}\beta _{1}+\beta _{2})q^{2}+(1895994\beta _{1}+312\beta _{2}+\cdots)q^{3}+\cdots\)
25.34.b.b \(10\) \(172.457\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(296\beta _{1}+472\beta _{2}+\cdots)q^{3}+\cdots\)
25.34.b.c \(12\) \(172.457\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{6}+\beta _{7})q^{2}+(158\beta _{6}-77\beta _{7}+\cdots)q^{3}+\cdots\)
25.34.b.d \(22\) \(172.457\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{34}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{34}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{34}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)